Are there any ways to lose in a "You can't lose the game" game?
In general in Magic: the Gathering, "can't beats can":


  101.2. When a rule or effect allows or directs something to happen, and another effect states that it can’t happen, the “can’t” effect takes precedence.


So Lich's Mastery and Platinum Angel prevail against Door to Nothingness. To win the game, you first need to get rid of the opponent's permanent. Or, in the case of Lich's Mastery, have a card that states that you win the game, like Battle of Wits. Lich's Mastery has a ruling below the card in Gatherer:


  While you can’t lose the game, your opponents can still win the game if an effect says so.


and that's the reason why Platinum Angel separately states "your opponents can't win the game".