Meaning of Dhamma for lay

Dhamma is universal and timeless hence does not undergo any changes, through people's understanding of the same may change due to experiences, views, perceptions, etc. General understanding like a person's understanding does undergo changes. The true understanding of the Dhamma happens at the experiential level, i.e., through meditations in which case this is in line with true reality which is universal and timeless.

What is Dhamma for lay person?

A lot of the suttas are intended for monks: see for example this answer.

How to know Dhamma in the way it was meant to be?

Perhaps answering that question would be the role of a teacher.

Is Dhamma same for all sentient , remain same over the period of time or does Dhamma undergoes change? Are there different versions of Dhamma?

I might be wrong but I think that Dhamma has (at least) two meanings or aspects:

• A description of what the world is, and how it works
• A description of what to do, or how to be or not to be, within the world

I think there are different answers to your question:

• To some extent, Buddhist Dharma changes -- or, at least, is augmented, with newer Dharma being added onto although not replacing the older Dharma -- see for example Three Turnings of the Wheel of Dharma.

• To some extent, Buddhist Dhamma is unchanging -- for example doctrine like this says that all Buddhas teach the same Dhamma:

  On one occasion, Thera Ananda asked the Buddha whether the Fundamental Instructions to bhikkhus given by the preceding Buddhas were the same as those of the Buddha himself. To him the Buddha replied that the instructions given by all the Buddhas are as given in the following verses

There's also a term upāya or upāya-kosalla, which I think is used to say that there are different teaching-aids.

Conventional: Upasaka (male layperson), Upasika (female layperson) lit. "attendant", "those who serve" denotes the follower or disciples of the Buddha, who are not monastics. As an assembling or in mixed groups called parisa (gathering)

Ideal: The not monastic part of persons of the Noble Sangha, the fourfold assembling: Monks, Nuns, lay men, lay woman, who have already attained one of the stages of "saintliness" (eight persons, divided in path and fruit attaining)

More maybe here Upāsaka and Upāsikā on Wiki, although Atma knows well that wiki is a very not so trustworthy place or out of conflicts rather blank in regard of issues which are often wrong introduced from mainstream Buddhisms. Topics that supports or touch the ego.

A list of famous Laypeople found in the Canon:

• AN 1.248 Chaṭṭhavaggo - male
• AN 1.258 Sattamavaggo - female

For whom are certain teachings?

There is no such as "Dhamma for this and that kind of person" outwardly things, but of cause there have been teachings given to Laypeople and teachings given to Monastics and teachings given to other ascetics ... So its always good to keep in mind the persons and the circumstance of certain talks. In matters of ideal, every teachings is of use and Dhamma for everyone nut not always of use if a person is bound to certain things. Useful source in regard of how to read the suttas: Befriending the Suttas, by Upasaka J. Bullitt:

As you read a sutta, keep in mind that you are eavesdropping on the Buddha as he teaches someone else. Unlike many of the Buddha's contemporaries from other spiritual traditions, who would often adhere to a fixed doctrine when answering every question [AN 10.93], the Buddha tailored his teachings to meet the particular needs of his audience. It is therefore important to develop a sensitivity to the context of a sutta, to see in what ways the circumstances of the Buddha's audience may be similar to your own, so you can gauge how best to apply the Buddha's words to your own life situation.

As you read, it can be helpful to keep certain questions circulating gently in the back of your mind, both to help you understand the context of the sutta and to help you tune in to the different levels of teaching that are often going on at once. These questions aren't meant to make you into a Buddhist literary scholar; they're simply meant to help each sutta come alive for you.

To whom are the teachings directed? Are they addressed to a monk [SN 35.85], nun [AN 4.159], or lay follower [AN 7.49]? Are they addressed to one group of people, while someone else within earshot actually takes the teaching to heart [SN 35.197]? Is the audience a large assembly [MN 118] or an individual [AN 4.184]? Or are the listeners followers of another religion altogether [MN 57]? What is the depth of their understanding? If the audience consists of stream-enterers striving for arahantship, the teachings presented may be considerably more advanced than if the audience has only a limited grasp of the Buddha's teachings [AN 3.65]. These questions can help you assess how appropriate a particular teaching is for you...(and many more good advises)

And the Dhamma is timeless akāliko

Sandiṭṭhiko akāliko ehipassiko | to be seen here & now, timeless, inviting all to come & see

As for the label(s) "Lay Dhamma", Lay-Buddhismus, Secular Buddhimus... such is a modern appearance which mostly rejects the necessary of the Sangha (monastic disciples) and believes on the maintaining of the Buddha Dhamma without the need and use of the Holy Life. Its a kind of Buddhism 2.0 and the main introduced way in modern and western countries where actually no real Sangha exists or have been established.

Becoming a lay person

With the refuge to the Buddha, Dhamma and the Sangha (of the Monks), people became and become lay followers. Although its usual suggested and more that good to take on the 5 precepts, it's not necessary to be called a Lay follower (Buddhist Layperson). Traditionally such a requesting/taking of refuge and precepts requesting/taking is made by asking Monks or Nuns who would recite and also explain the certain texts. If not available, one could also consulate a knowledgeable and virtuous lay person or do it for one self (how ever, it goes deeper and drives one more if made in the traditional way)

See also the stages of being a Lay-Buddhist: Mahanama Sutta: Being a Lay Buddhist

The practice of lay people:

The practice of laypeople is usually: - Giving or Generosity (Dāna): material giving, and meritorious deeds Transference of merit, and Rejoicing in other’s merit. - Moral conduct or Virtue (Sīla): Virtue, incl. the meritorious deeds Reverence, and Service. - Meditation or mental Development (Bhāvana): incl. the meritorious deeds Expounding (discussing) the Dhamma and Listening to the Dhamma.

All this deeds are supportive or include the main task: Correcting one’s view.

If one changes the way of live to somebody who lives from the alms of the country, then Dana - the material giving - is no more necessary (even not possible, since one has given up all unnecessary and does no more amass material possession) if practicing seriously and straight forward.

Vinaya for Laypeople

There is a Sutta where the Buddha taught a young man about the use of his ritual traditions he uses to perform. In this Sutta the Buddha described the good behavior, moral and duty of a lay person: Sigalovada Sutta: The Discourse to Sigala

What can be attained on this path?

Actually all path and fruits can be attained on this path, even to the highest attaining, Arahatship (AN 6.119-139). How ever, if one reaches the highest level, one is no more able to live and maintain an more or less normal live and would seek for the way of the Holy Live, homelessness. If such can not be attained, the Canon reports that people will leave there last body with a week.

Overview Anagarika Isi Dhamma (before Monk) gives a nice and easy understandable explaining in general in his The laity practice

Who is a lay person?

Finally, among the people who adhere to the dhamma, all those who are not bhikkhus, or sāmaṇeras, or nuns are laity. We can divide lay people into three categories:

• There are some laity who, although approving Buddha's word, only dedicate their life a little, or not at all, to the practice of the dhamma. They like to claim that they are Buddhists, but do little else than run after pleasures and engage in business activities; if they observe one or two precepts, it is only because it is easy for them; they don't want to dedicate any effort to the rest. Even though they claim to be inclined to meditation, they convince themselves that they never have any time to practice it.
• There are also lay people who try to dedicate more time and effort to follow a way suitable to the development of knowledge (of reality). They more or less observe the five precepts (sometimes the eight), they like everything that concerns the dhamma aesthetically (monuments, statues, ceremonies), they readily spend time reciting texts dealing with Buddha's teaching, watching the quality of their actions, regularly making donations, attending meditation sessions, and sometimes, taking ordination for a short period.
• Finally, there are laity who, within their possibilities, try their best to progress quickly and effectively on the path to the cessation of suffering. These ones very regularly train in being generous, in being vigilant and in applying full mindfulness. Their observance of the five precepts, if not eight, is scrupulous. Some of them even intend to lead a monastic life permanently.

(Note: this answer has not been given with the agreement to be means of trade or the purpose of/for trade and/or keep people trapped and bound. How you handle it lies in your sphere, but does not excuse the deed here either.)