As expected value ≠ expected utility, it's not the case that you should always buy a ticket if expected value is positive. It's a standard result that people actually treat the utility of wealth roughly logarithmically: i.e. that it's better to have a net worth of $1,000,000,000 than $100,000,000, but not that much better compared to how much better $100,000,000 is than $1000 net worth.

To simplify the lottery situation in the case of extreme probabilities and payouts, say that Omega offers a lottery only to you (no worries about split jackpots), in which there are exactly 1,000,000 tickets, each costing $1, and among them there is one winning ticket that pays out $2,000,000.

Now if you can scrounge up a million dollars to buy every ticket, you make a tidy $1 million profit (less interest from your backers) with zero risk, so the expected utility is very positive for this strategy.

If, however, you can only get $100,000 together, you shouldn't buy any tickets (unless you're a millionaire to start), since the utility to you of a 90% chance of losing $100,000 (and having a pretty crappy life being so far in debt) outweighs the utility of a 10% chance of winning $2 million (and a nice standard of living).