"e4, best by test" – lichess' analysis agrees

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I've seen this problem before too. I think it has to do with Stockfish analysing a position which is not actually on the board, and then the lichess framework translating the moves Stockfish gives onto the actual position (imagine if Stockfish would like the move Rg8-g6 in some position and therefore output "g8g6," lichess would write "Ng6" because there's currently a knight on g8 and Stockfish apparently wants to move it to g6). The position Stockfish was actually analysing (maybe the end of the game you were analysing?) was probably mate in five for white. Long story short, the engine isn't always aware of the position on the analysis board and this should probably be updated more often.

chess has been solved!

Yes and "d4 = dull & drawish" from the same source.