The plural form of: One's life work

I can see that what you are trying to do is use the plural and yet also apply the possessive. When a word ending with "s" is possessive, just add an apostrophe to the end of the word.

Here is a quote from http://data.grammarbook.com/blog/apostrophes/apostrophes-with-words-ending-in-s/

Rule 2: To show plural possession of a word ending in an s or s sound, form the plural first; then immediately use the apostrophe. Examples: the classes’ hours, the Joneses’ car, guys’ night out, two actresses’ roles...

So the spelling you're looking for is:

"They have made it their lives' work..."

What about "their life-work"? I don't know whether this word composition exists or is usual in English, but it is usual in German (Lebenswerk).

Amendment

Though my COD has only life's work the BNC gives 9 examples for life work (without hyphen). One example is:

• It was at his home that Galileo renewed his life work, that on mechanics and motion.

http://bnc.bl.uk/saraWeb.php?qy=life+work&mysubmit=Go

Plural: Probably "they + their life work".

Of OP's four suggestions, only the first...

Their life's work

...is remotely credible, on the grounds of basic grammar.

The second fails because live isn't a noun. Only nouns can take the Saxon genitive 's.

The remaining two fail because they don't include any possessive marker at all. It's an integral part of the "base form" that isn't dependent on "plurality", so I see no justification for discarding it. Besides which, lifes in #4 isn't a valid plural except in special cases such as several still lifes (see Wikipedia).

In OP's specific context it's reasonable for work to be in the singular, because it applies to a single collaborative effort (the software company). But even where the reference is to multiple, independent efforts, people usually don't pluralise to works...

But seven artists stood out: Braque, Chardon, Duchamp, Hals, Peale, Sloan, and Trumbull produced 8% of their life's work in the 80s.

...dozens of scientists, spiritual leaders, and social activists make the telling of a sacred evolutionary story part of their life's work.

Having said that, I think pluralising is sometimes a perfectly justifiable choice...

[We] picked cartoonists whose life's works would be most familiar to the average citizen.

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TL;DR: the collocation life's work is effectively an established single syntactic unit. You can modify the entire thing by adding a pluralising s (although in fact most people don't, even where semantically justified), but you can't tinker with the internal structure, so life's must remain unchanged.

Which is semantically sensible anyway, since each individual life is normally only dedicated to a single work, even if you're actually talking about the "works" of multiple "lives".

There doesn't appear to be a universal consensus on this point. I would suggest that the OP chooses the form he or she prefers and remain faithful to that.

CDO life's work noun [U] (US lifework)

Your life's work is the work that is most important to you and to which you give a lot of time and effort: Her garden was her life's work

1. Without the possessive apostrophe (an unusual construction)

   • Now, at mid-life, at an average age of 44, the subjects can be considered to be pretty well established in their life work _source

   • At this point, many individuals become concerned about their generativity, their life work, and connecting to social or spiritual realms outside of the self _source

2. The singular noun with the possessive apostrophe i.e. life's

   • After concerns about money, the next major obstacle that holds people back from taking up the quest for their life's work is fear of breaking away from the pack. _source

   • Reflecting upon their life's work, Thuli and Catharine envisaged a multigenerational timeline in which their children and grandchildren would benefit from their hard work. _source

3. The plural noun with the apostrophe after the suffix -s; i.e. lives'

   • They imagined it as a time for reflection and recollection of their lives' work and their relationship together. _source
   • Women listed their children as a validation of their lives' work _source

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It can also be written as one word

lifework noun
1. the complete or principal work, labor, or task of a lifetime.
1870-75; life + work

• The introducer explained that my research had disproved part of my adviser's lifework, and the shock had killed him
• It is also being used with adults who want to clarify their lifework objectives and perhaps make mid-life career changes.

4. As an 'uncountable' noun i.e. lifework

   • how these individuals, with different backgrounds and located in different situations, go about organizing their "lifework" and how this ties into their access to social services... _source

   • ... what we want is teachers who have made teaching their lifework, [...] and the number of those who make teaching their lifework will soon be greater than those who consider it simply a business source

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N.B The expression their lives work is a little unusual but nevertheless grammatical. In this instance, work is used as a verb meaning to produce a desired effect or result; to succeed. E.g. my deepest satisfaction in work is to give people insights that help their lives work better