Playing on Lichess directly from the chess computer has been possible since version V4.01E. In addition to the normal game modes, the function supports your own friends list and also the Swiss and Arena tournaments.
A connection to Chess.com directly from the chess computer is unfortunately not possible, since Chess.com does not have an open interface and thus cannot be controlled by the ChessLink App. A game on Chess.com is of course possible via the Millennium Mephisto boards in connection with the ChessLink module and a mobile Android device.