If a Buddhist believes lay life is not ideal for the practice, why does he or she continue?

Whether one is a lay practitioner or a monk, either way the key to progress is the daily practice. Either can meditate twice a day, do walking meditation, do karma work, do charity work, and raise their consciousness. Maybe the idea that the monastery is better than lay life is a concept that may be true or not true. Listing the jobs in each place and the challenges each offers may give a better idea of the demands of a monk or lay person. The Buddha did not give higher value to one over the other. Many lay person's attained enlightenment in Buddha's day. Perhaps the real question is one that must be asked within where there are no words or concepts and wait for an inner response: What is my calling in life? What have I come here to do? Why have I come here? What can I do that will most fulfill that aim?

By allowing the beginner's mind, the nirvana consciousness to grow, these answers may appear when the time is ripe.

Your use of the word "absurd" in the original title makes me wonder whether you've been exposed to 20th century nihilist philosophy.

"Absurd" comes from a Latin word meaning "dissonant" and it refers to the dissonance between man's expectations and his actual experience.

That's kind of cool (it's maybe the second noble truth) but it's still a description of the problem, and not of the solution.

Note that the Buddha spoke again both extremes: eternalism and nihilism.

I could try to suggest two remedies:

• Learn more about life in a Sangha -- for example you could read http://plumvillage.org/category/blog/ without leaving your home
• Learn more about lay Buddhist life -- for example, the book described in this answer could be interesting

There are also some half-way measures, e.g. lay people visit or work with Sanghas.

Speaking from a general point-of-view, if a Buddhist knows that the lay life is not ideal, what barriers (overt and inconspicuous) are preventing them from seeking and living the monastical life.

This isn't quite what you were asking, but one answer is that to be accepted they might require you to be in reasonable health, and not too old (e.g. less than 50)

Also your basic question seems to be "why don't I act rationally?" Well that's a good question but maybe it's normal for human to have habits, including bad habits, and developing discipline and rationality and insight etc. is non-trivial.

There's a (non-Buddhist) poem addressed to Siva (named "Ramanatha" in the poem),

If this is my body
Would it not follow my will?
If this is your body
Would it not follow your will?
Obviously, it is neither your body
Nor mine:
It is the fickle body
Of the burning world you made,
Ramanatha.

How can they be overcomed ?

There's a little voice in my head that replies, "First you must have that intention (to overcome them)."

I suppose a canonical answer is the "noble eightfold way" (see for example here and here): that's the path to liberation. You start with Right View (seeing your situation properly), then Right Intent (wanting to act appropriately for that situation), etc.

And even a little is better than none IMO: doing away with ill-will, intending to be harmless, etc.

You might like to read The Intention of Renunciation since that's what you seem to be asking about,

The Buddha does not demand that everyone leave the household life for the monastery or ask his followers to discard all sense enjoyments on the spot.

Maybe you don't want to lose happiness (by losing work, hobbies, social, etc.). Maybe a key then is to replace these forms of happiness, not with nothing but with other causes of happiness: e.g. equanimity (freedom), good will, etc.

Two reasons come to mind; one practical, the other metaphysical.

Practical

What you describe is no different from how we live our lives all the time. We want things but don't want to do the work for them.

• We want to lose weight, but don't want to exercise.
• We want to learn a skill, but don't want to spend time practicing it.
• We want happiness, but don't want the changes required to bring it about.

I think this is the same phenomena. We want the fruits of Nirvana, but don't want to give up our attachments.

Also, there is something compelling about Samsara, otherwise it wouldn't be such a challenge to let it go. Besides, I think many people who superficially believe in Samsara do not believe it deep down.

How to overcome it? Well, mindfulness of Samsara. If you can really see this life as unsatisfactory, then the problem should solve itself. However, the key is seeing, not intellectual assent. We intellectually assent to many things that we don't really see. Can you honestly encounter your experiences in every moment, reflect on them, really SEE Samsara? That you can get some glimpses of Nirvana along the way can serve as a useful stick and carrot corrective.

Metaphysical

Many Buddhists believe in rebirth. The quality of one's rebirth is commensurate to one's practice here. Therefore, even if a lay life is not ideal, one may practice to ensure a more favorable rebirth wherein one can practice more rigorously and at some point down the line achieve Nirvana.

How to correct this? Abandon believe in rebirth! Of course that's easier said than done for those who have that worldview.

"There is the case, great king, where a Tathagata appears in the world, worthy and rightly self-awakened. He teaches the Dhamma admirable in its beginning, admirable in its middle, admirable in its end. He proclaims the holy life both in its particulars and in its essence, entirely perfect, surpassingly pure.

"A householder or householder's son, hearing the Dhamma, gains conviction in the Tathagata and reflects: 'Household life is confining, a dusty path. The life gone forth is like the open air. It is not easy living at home to practice the holy life totally perfect, totally pure, like a polished shell. What if I were to shave off my hair and beard, put on the ochre robes, and go forth from the household life into homelessness?'

"So after some time he abandons his mass of wealth, large or small; leaves his circle of relatives, large or small; shaves off his hair and beard, puts on the ochre robes, and goes forth from the household life into homelessness.

"When he has thus gone forth, he lives restrained by the rules of the monastic code, seeing danger in the slightest faults. Consummate in his virtue, he guards the doors of his senses, is possessed of mindfulness and alertness, and is content.

Samaññaphala Sutta (DN 2)

Also, this is what the Boddhisattva thought :

"Why wouldn't it have, Aggivessana? Before my Awakening, when I was still an unawakened Bodhisatta, the thought occurred to me: 'Household life is confining, a dusty path. Life gone forth is the open air. It isn't easy, living in a home, to practice the holy life totally perfect, totally pure, a polished shell. What if I, having shaved off my hair & beard and putting on the ochre robe, were to go forth from the household life into homelessness?'

"So at a later time, when I was still young, black-haired, endowed with the blessings of youth in the first stage of life, having shaved off my hair & beard — though my parents wished otherwise and were grieving with tears on their faces — I put on the ochre robe and went forth from the home life into homelessness.

Maha-Saccaka Sutta (MN 36)

This is to support Sankha Kulathantille's answer - which I think is reasonable and in line with the Dhamma.

Also, I think you should consider reading the Samaññaphala Sutta, if you haven't done so already.

When I think about it, I feel like the monastic life is the only way to proceed yet I don't follow through with it.

While the ideal monastic life is considered the swiftest route to Nibbana, don't overly romanticize the monastic life today. It depends on where you are. Many monastics in Asia perform a purely cultural role fulfilling funeral rites and other customary rituals, some have abandoned the quest for enlightenment and taken up nationalistic causes.

Likewise don't overly put down a household life as being impractical to the practice. If you are disciplined and dedicated enough you can practice at home, perhaps finding encouragement from other like minded friends, and with the guidance of an experienced and knowledgeable teacher. There were many householders who attained states of sotapatti, sakadagami and anagami and continued to remain householders even after.

Why does he or she continue?

Because of clinging. Clinging to family, clinging to lovers, clinging to property, clinging to comforts, clinging to all kinds of sensual pleasures which the monastic life wouldn't have.

How to overcome it?

You have to develop Nekkhamma Sankappa of the noble 8 fold path. Take a timeout to think about what you've really been trying to do every day, your whole life. Being yourself subjected to birth, sickness, aging, death etc. which cause suffering, you are trying to attain satisfaction by chasing after other things which are also subjected to birth, sickness, aging and death. This is called the ignoble search. Think of the absurdness of doing the same thing over and over again, when it can never give you the intended outcome. Pay careful and wise attention to the signs of Anicca, Dukkha, Anatta in life. What made prince Siddhartha decide to leave the lay life? Seeing an old man, a sick man, a dead body, a hermit. We see the same things too. But we rarely pay wise attention. We rarely think that we are also subjected to the same misery. Even if we do think that, it would just be a passing thought. It wouldn't be strong enough to break the bonds of lay life. It wasn't a passing thought for prince Siddhartha. He thought about what he saw even after returning to the palace. He cultivated his mind with Nekkhamma thoughts, which eventually became strong enough to make him decide to leave the lay life to do the noble search. i.e. to seek the unborn, unaging and the deathless element.