I was wrong when I said that switching life is not the same as gaining life. Per MotM ruling: When the life totals are exchanged, each player gains or loses the amount of life necessary to equal the other player's previous life total. For example, if player A has 5 life and player B has 3 life before the exchange, player A will lose 2 life and player B will gain 2 life. Replacement effects may modify these gains and losses, and triggered abilities may trigger on them.
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Doing a little further research. From MotM ruling: If an effect says that a player can't lose life, that player can't exchange life totals with a player who has a lower life total; in that case, the exchange won't happen.And Lich: If you would gain life, draw that many cards instead.Lich doesn't prevent you from gaining life, it just swaps life gain out for card draw. I think it is still legal.
I've just started looking into Lich decks, and I know I am responding to this two years after it was posted knowing chances are slim anyone will read this.That said, I believe the above statement is incorrect. I believe you can switch life totals with someone. Switching life totals is not the same thing as gaining life - gaining life is a specific keyword function. Using Mirror Universe + Lich was a very common tactic back in the day.So it would seem that Magus of the Mirror is the equivalent of Mirror Universe. CMC is the same too.