So a couple things... technically you can't swap life totals because you can not gain life, the draw ability of the Lich. I could be mistaken but I believe it works that way. As for the Lich's Mirror, you would not get the Lich after you've started over, it would get shuffled back into your deck. It falls under the "permanents you own" category.Addendum; you can not swap life totals with someone who has more* life than you. The only useful card I've used with that in mind is Death's Shadow, where going into the negative's actually increases its power and toughness
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