Morere is the second person present imperative, while moriaris is the second person present subjunctive. What we need here is the subjunctive. Since your tattoo already says Fac ut vivas, you can add ne moriaris (lest you die). The subjunctive is necessary in the second clause in order to imply what will happen lest you don't fulfill the requirement of the first clause.
Fac ut vivas, ne moriaris - literally meaning "Make it so that you live, lest you die."
It would have been possible to coin a similar phrase using the aut conjunction, as in Aut vive aut morere (Either live or die). But since the beginning of the phrase is already set in stone, its remainder must be complementary. Ne and ut being of the same category, I think they complement each other nicely here.
Allow me to correct my colleague, his sentence should read:
Aut vive aut morere
Viva is a different word.
I agree with his suggestion, however, as it does provide a nice structure. I think there may actually be a rhetorical term for this, but I can't put my finger on it. It reminds me of chiasmus, but I know that's incorrect...
"Lest" is a conjunction that is placed before a clause describing something that we wish to avoid. For example, "You should eat, lest you become skinny". In our case, "lest you die" means "so that you don't die".
By the way, how is the winter up there this year?? Not too harsh, I hope.