I just wanted to say: Vegetarians will most likely live longer than other sims. If you scroll over the trait in live mode/CAS, it says that they live longer. But apparently in some cases they don't.
The general theme in this thread has been that death by old age is random, with things like traits and athletic challenges decreasing the chance. I'll toss out some arbitrary numbers so you have an idea of what I'm talking about:
Let's say that the base chance of death by old age is 5% per day, and the vegetarian and Marathon Runner challenge both decrease the chance by 1% each. You have 2 sims: Sim A has both by the time they're an elder, and Sim B has neither. That gives a 3% and a 5% cumulative chance per day respectively that Grim will stop by to say "Hi" to either of them.
10 days pass. That gives Sim A a 30% chance that today is their last day, while Sim B has a 50% chance. It is entirely possible that through an unfortunate "roll of the dice" that Sim A will die but Sim B won't, even though Sim B actually has a better chance of dying. It's also entirely possible that Sim B will continue to get lucky, and will live quite a bit longer that Sim A.
It's very likely that the numbers are smaller than what I used, and will change depending on the lifespan you're playing on. But that's the general idea of how it seems to work.