Lethe Lake

A face-up plane card that's turned face down becomes a new object with no relation to its previous existence. In particular, it loses all counters it may have had.

If an ability of a plane refers to "you," it's referring to whoever the plane's controller is at the time, not to the player that started the game with that plane card in their deck. Many abilities of plane cards affect all players, while many others affect only the planar controller, so read each ability carefully.

If you don't have ten cards in your library, you'll put all the cards in your library into your graveyard. The same is true if the targeted player doesn't have ten cards in their library.