Okay so specific scenario here. If I have the card Lich's Mastery and my opponent casts their second Approach of the Second Sun, what happens? I attached pictures of each card.
Unlike with Platinum Angel, your opponents can still win the game despite you controlling Lich's Mastery. Moreover, Approach of the Second Sun contains an effect that makes a player win the game (C.R. 104.2b). And the "game ends immediately when a player wins" (among other circumstances) (C.R. 104.1). But nothing in the comprehensive rules explicitly states that a player who would win the game makes all other players lose the game, with the exception of multiplayer games using the limited range of influence option. In such games, Approach of the Second Sun's effect of making a player win the game "instead causes all of that player's opponents within the player's range of influence to lose the game" (C.R. 104.3h) — and in such cases, you won't lose the game this way thanks to Lich's Mastery (C.R. 101.2, 109.5). See also this thread.
In a duel and multiplayer games without limited range of influence, the fact that you can't lose doesn't keep the opponent from winning, so a "you win" effect still lets them win the game.
Otoh, in a multiplayer game with limited range of influence, a "you win" effect makes all opponents within the range of influence lose the game. If you can't lose the game, you remain in the game, and the game continues.
104.3h In a multiplayer game using the limited range of influence option (see rule 801), an effect that states that a player wins the game instead causes all of that player’s opponents within the player’s range of influence to lose the game. This may not cause the game to end.
Otoh, in a multiplayer game with limited range of influence, a "you win" effect makes all opponents within the range of influence lose the game. If you can't lose the game, you remain in the game, and the game continues.
Former Rules Advisor
"Everything's better with pirates." - Lodge
(The Gamers: Dorkness Rising)
"Any sufficiently analyzed magic is indistinguishable from science."
(Girl Genius - Fairy Tale Theater Break - Cinderella, end of volume 8)