Generally this will depend on the character in question! If a character needs to eat to survive in canon, they'll need to do so on the Barge; if they don't need to eat in canon, they won't have that necessity foisted on them on the Barge. A character who falls into the former category could theoretically starve to death without intervention.

That said, we're always up for trying to work things out on a case by case basis, particularly where powers and supernatural needs are concerned. I peeked at the info on this journal, and am seeing that Lara is a character for whom sex is like food; if you're concerned about her "starving" to death onboard due to lack of sexual options, we could absolutely work with you to come up with a fix (negating the sex-for-survival need entirely, significantly lengthening the amount of time she can go without it, something else???).