The word life has a definition in a dictionary,
a way of living or a particular part of someone's life
In the following sentence, should I use singular form or plural form of the word life?
Rich men or women can enjoy luxury lives which are attractive to a great deal of people.
As Chryslis says, by "life" here you really mean "lifestyle", though I don't see a problem in using the word "life". And, yes, both singular and plural work, depending on whether you are thinking of each rich person having a unique life(style), or whether you think of them as all sharing one grand life(style).
You should say "luxurious" rather than "luxury" -- the sentence calls for an adjective modifying "life" rather than a noun. "Luxury" is sometimes used as an adjective, e.g. "a luxury yacht", but that's awkward here.
Also I think it's aswkward to say "a great deal of people". "Great deal" in this sense is normally used with uncountable nouns -- "a great deal of money", "a great deal of water", etc. For countable nouns we usually say "a great many" or simply "many" (or any of hundreds of other expressions with similar meaning).
So:
Rich men or women can enjoy luxurious lives which are attractive to a great many people.
Rich men or women can enjoy a luxurious life which is attractive to a great many people.
In this case, the word lifestyle is more suitable than life. Whether it is singular or plural depends on whether you are talking about the generic "luxurious lifestyle" that all rich people share or discussing the various ways in which rich people could enjoy "luxurious lifestyles", such as through travel, high society, patronage of the arts, and so on.
