Should one twin kill themselves if the other twin won the lottery

Ah, now I understand your setup. Thank you for simplifying it for me. So the issue here is whether to count multiple copies as one person or separate ones, and your argument with twins is pretty compelling... as far as it goes. Now consider the following experiment (just going down the LCPW road to isolate the potential belief-in-belief component of the MWI):

The lottery is setup in a way that you either win big (the odds are small, but finite) or you die instantly and painlessly the rest of the time, with very high reliability, to avoid the "live but maimed" cop-out. Would you participate? There is no problem with twins: no live-but-winless copies ever exist in this scenario.

Same thing in a fantasy-like setting: there are two boxes in front of you, opening one will fulfill your dreams (in the FAI way, no tricks), opening the other will destroy the world. There is no way to tell which one is which. Should you flip a coin and open a box at random?

You value your life (and the world) much higher than simply fulfilling your dreams, so if you don't believe in the MWI, you will not go for it. If you believe the MWI, then the choice is trivial: one regular world before, one happy world after.

What would you do?

Again, there are many standard cop-outs: "but I only believe in the MWI with 99% probability, not enough to bet the world on it", etc. These can be removed by a suitable tweaking of the odds or the outcomes. The salient feature is that there is no more multiple-copies argument.