do does

in this sentence 'do' hinges on 'lives' and not 'everyone'. consequently, the do form applies here.

A, did you mean that each person has more than one life? Everyone's is singluar, mean each person has... and then you have a plural word, lives. If you want to, post the entire sentence for us to look at.

When asking what (do or does) item 1, item 2 and item 3 have in common? Which do you use: do ro does?

What DO these three items have in common, so use "do."

You probably shouldn't say "everyone's lives of faith" in the first place.  It sounds awkward to me.  I would say "People's lives of faith do not affect..."
(It's "do" because "lives" is plural.)

when do you use 'do' and when do you use does?

I do

You do

He, she, it does

We do

They do

-- So, third-person singular (he, she, it) uses "does."

we use DO with I, you, we and they.

we use DOES with he, she, it, everybody, everyone, nobody, anybody, etc.

>everyone's lives of faith (do/does) not affect...

The sentence is incorrect. "Everyone" is always singular. (The clue lies in "one". "Every one".)

Therefore, it should be "everyone's life of faith does not affect...