While you control, Liliana’s Undead Minion, nothing can cause you to lose the game. You won’t lose from having 0 or less life, drawing a card from an empty library, having ten or more poison counters, and so on. However, your opponents can still win the game if an effect says so, such as with the ability of Wowzer, the Aspirational.

If you control Liliana’s Undead Minion in a Two-Headed Giant game, your team can’t lose the game.

You can activate one of Liliana’s Undead Minion’s loyalty abilities the turn it enters the battlefield. However, you may do so only during one of your main phases when the stack is empty. For example, if Liliana’s Undead Minion enters the battlefield during combat, there will be an opportunity for your opponents to remove it before you can activate one of its abilities.