This game should have been draw by move 61. But lichess error!

No lichess error at all:
FIDE Laws of Chess
6.9 Except where one of the Articles: 5.1.a, 5.1.b, 5.2.a, 5.2.b, 5.2.c applies, if a player does
not complete the prescribed number of moves in the allotted time, the game is lost by
the 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.

In this case a series of legal moves exists that leads to checkmate in the corner.
So play goes on until 3 fold repetition or 50 moves rule or players agreeing on a draw or checkmate or flagging.

You can still checkmate, for example imagine setup:
White: Kh1, Bg1
Black: Kg3, Be4#

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