To not hear both, disable lichess sound in lichess preferences.
This is for lichess.
This will change all the sounds to be like chess.com (castling not sounding properly since there is no dedicated castling sound for lichess yet, maybe later) .
You only need to install this.
To also have similar piece designs you can use stylish plugin and search for example : Lichess Pieces:Wood(Chess.com) and Lichess Board:Walnut(Chess.com) in their search ui.
Credit to https://github.com/JakubCisowski/lichess-chesscom-soundpack for the code ( i only modified timeout if i recall correctly)
How to use it:
Disable Lichess sounds in top right corner to not hear both sounds
