Socialists love lotteries not because of their regressive nature, but rather because they reinforce the idea that success is due to chance rather than integrity, excellence and good ideas.
My suspicion is that the real reason they like lotteries is because they need unequal distribution of wealth in order to demogogue their particular brand of politics. The last thing the Dems would want is to solve the problem of poverty. It would put them out of business.