I heard it's never intended to be the same since initial rating for Lichess and chess.com respectively is 1500 and 1200. So they should have 300 rating difference on average. Quite fitting with what the other commenter claims actually.
If everything else was the same, and people play enough games they will average out to the same elo.
The difference is caused by many factors. People don’t play enough games to sink to their real elo, the player pool is different, and you gain/lose fewer points per game with Lichess’s elo algorithm.
Also I can't really prove it mathematically but I guess average ELO would also hover on the starting ELO. Because I can't see why it would hover anywhere else and any ELO gained would be lost by someone else.
When I started playing I believe chess.com let you select whether you’re beginner, intermediate or advanced and your start elo was based on that. Could be wrong, and it could’ve changed since.