According to rules, he can checkmate you by some sequence of moves so the result is a win. Lichess really should make a separate section where they would explain these things because like half of the forum posts are about this...
FIDE rules, article 6.9: Except where one of Articles 5.1.1, 5.1.2, 5.2.1, 5.2.2, 5.2.3 applies, if a player does not complete the prescribed number of moves in the allotted time, the game is lost by that player. However, the game is drawn if the position is such that the opponent cannot checkmate the player’s king by any possible series of legal moves. - He can checkmate you by a sequence of moves
With pieces on the board, even though the pawn chain is locked, there will be a sequence of legal moves that result in a win.
The 2nd position is a draw. A Fortress, that Comps do not understand. It seems the issue is being worked on by programmers (not lichess) to recognize the draw, besides better evaluating positions that programs will evaluate as winning, but in fact are dead drawn or sometimes even losing.