You can certainly look at lotteries that way. But the "friction" you mention is typically rather large. You would probably do better to go and play roulette, or make repeated risky stock-market investments. For that matter, some of your "MWI-selves" will in any case just happen to receive big piles of money from eccentric millionaires, surprisingly successful employers, and the like.
So there's nothing very special about lotteries, and I suggest that the way to minimize friction and get more money to your possible future selves is to choose random money transfer schemes other than lotteries.
Which random money schemes do you think would be best at this?
Or, for a tougher challenge: for people with relatively limited resources to spend on such a project, which such schemes have a reasonably low barrier to entry?
I haven't been able to find the source of the idea, but I've recently been reminded of:
This is, of course, based on the Multiple Worlds Interpretation: if the lottery has one-in-a-million odds, then for every million timelines in which you buy a lottery ticket, in one timeline you'll win it. There's a certain amount of friction - it's not a perfect wealth transfer - based on the lottery's odds. But, looked at from this perspective, the question of "should I buy a lottery ticket?" seems like it might be slightly more complicated than "it's a tax on idiots".
But I'm reminded of my current .sig: "Then again, I could be wrong." And even if this is, in fact, a valid viewpoint, it brings up further questions, such as: how can the friction be minimized, and the efficiency of the transfer be maximized? Does deliberately introducing randomness at any point in the process ensure that at least some of your MWI-selves gain a benefit, as opposed to buying a ticket after the numbers have been chosen but before they've been revealed?
How interesting can this idea be made to be?