How does one decide whether one lives a lay married life or a celibate life?

If you are a practicing Buddhist and willing to go all the way, You can reach all Jhanas staying married. Even reach Anagami status being married. All you need to do is obey 5 precepts, guard your senses, follow a strict schedule and meditate.

In between times it’s up to you.

However, I don’t recommend becoming a monk until you reached a Jhana. In my opinion being a monk without any serous practice is wast of life.

I think at some point one becomes humiliated & ashamed of sexuality to the point where it's no longer an option. Hiriottapa just kicks in due to development, you realize that you don't ever want to feel that shame & regret and are unable & unwilling rationalize it otherwise even if the world thinks it's the norm you see it as sick.

They became lustful, and their bodies burned with fever. Due to this fever they had sex with each other.

Those who saw them having sex pelted them with dirt, ashes, or cow-dung, saying, ‘Get lost, filth! Get lost, filth! How on earth can one being do that to another?’ And even today people in some countries, when a bride is carried off, pelt her with dirt, ashes, or cow-dung. They’re just remembering an ancient traditional saying, but they don’t understand what it means.

What was reckoned as immoral at that time, these days is reckoned as moral. The beings who had sex together weren’t allowed to enter a village or town for one or two months. Ever since they excessively threw themselves into immorality, they started to make buildings to hide their immoral deeds.https://suttacentral.net/dn27/en/sujato#dn27:16.16

Just as a young woman — or man — fond of adornment, would be horrified, humiliated, and disgusted if the carcass of a snake or a dog or a human being were hung from her neck; in the same way, if evil, unskillful thoughts — imbued with desire, aversion, or delusion — still arise in the monk while he is attending to this other theme, connected with what is skillful, he should scrutinize the drawbacks of those thoughts: 'Truly, these thoughts of mine are unskillful, these thoughts of mine are blameworthy, these thoughts of mine result in stress.' https://www.accesstoinsight.org/tipitaka/mn/mn.020.than.html

Don't remember which text this last one is from but it's vinaya iirc

the Buddha admonishes him thus: “It is better for you to have put your manhood in the mouth of a venomous snake or a pit of burning charcoal than a woman.”

So yea, eventually this all sinks in and what was an option is no longer an option. One at some point has to accept that it's a serious mental disease and then straighten out what is crooked by means of development of wholesome qualities.

In practical terms my advice is to continuously put yourself in situations where you can attain seclusion, even if you fail you make that the general resolve, time and again, having conflicting desires you can support the one and not the other by relentlessly trying to attain pleasure which isn't worldly by making that opening.

When you have won seclusion and a pleasant abiding you protect that and you then won't be tempted by sensuality.

I am very conflicted between a lay married life and celibate life of serious practice. Anybody have the same dilemma? How did you solve it?

Ultimately it's a decision that only you can make for only you'd know the priority of Dhamma practice vs. other lay life responsibilities. There's nothing wrong with a married lay life, it's just that it won't provide you the same amount of freedom in terms of of time and space to dedicate to Dhamma practice. Once you've decided to make the big plunge into married life, you'd better be prepared and ready to sacrifice much of your own time dedicating to a whole new set of extra responsibilities: perform duties of love and care to your spouse, parental duty to your kids, various duties not only to your side of the family but also your in-laws' side of the family, various household maintenance chores, etc.

Firstly, you should avoid having a romanticized view of either the lay married life or the celibate monastic life.

Being a married person, you may find that your spouse, children and in-laws may often not be in line with your wishes and expectations, and may be a source of grief.

If you read the book "The Broken Buddha" by S. Dhammika, you will find that many monastic communities today are not living up to the standards of the Buddha's Sangha, to put it mildly.

Secondly, you can however, try to become an anagārika or novice monk (sāmaṇera) and try out the monastic life for a short time (maybe 1 to 3 months), as a trial, by staying in a monastery under the guidance of a teacher. In the end, you may find that this does not suit you, or the other way round. It's a practical way to guide your decision-making.

If one is married, one can first understand that desire is more often asymmetrical than not. One can also observe resentment arising out of asymmetrical desire.

Asymmetrical desire therefore provides an opportunity to explore the problem posed. For example, suppose that one has desire. Then one can consider whether that desire is asymmetrical or not. And if it is indeed asymmetrical, then we can give it up. Doing this puts one gently on the path to restraint and ultimately celibacy out of consideration for others. It is also serious practice that can gently change a married relationship to one of understanding and consideration absent lust. In other words, rather than fighting the daunting dilemma posed, one addresses it day-by-day within that day's context, moment by moment, breath by breath.

MN8:12.10: ‘Others will be covetous, but here we will not be covetous.’

Relinquishing asymmetrical desire for shared sensual pleasure is a small step that can help one start the practice of seclusion from sensual pleasures altogether. Seclusion from sensual pleasures is required to proceed on the Noble Eightfold Path. It is required for immersion, for jhana:

MN8:4.1: It’s possible that a certain mendicant, quite secluded from sensual pleasures, secluded from unskillful qualities, might enter and remain in the first absorption, which has the rapture and bliss born of seclusion, while placing the mind and keeping it connected.