I'm in a similar boat as the other posters (2050-2100 lichess, 1400 USCF). The median active rating for USCF is around 1200 and likely much higher if you don't include scholastic players, so if we compare against the OTB pool, "2000 lichess" is probably closer to top 50% than 2%
Put another way, looking at chess.com users, there are ~6 million people who would count as the top 3 percent. Difficult to achieve, yes, but if 6 million people can achieve it, it’s not really a “humble brag,” it’s just a statement.
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.