Two Easy Ways to Improve Your Lichess Rating

There's two things to do.
1. Avoid rematches
2. Only play tournaments.

Reason to Avoid Rematches

This is pretty straightforward. Do you want to lose to a cheater once, or do you want to lose to the same cheater repeatedly? Better to just fight another random player. Don't let your anger make you demand a rematch.

Reasons to Only Play Tournaments

Tournaments allow access to matches against higher-rated players. Lower-rated players are more likely to cheat, at least according to popular opinion. I think that's probably true. The problem is, when you use the Lichess auto-matching feature, you get auto-matched against similar-rated opponents. Here's evidence of that from my Chess Insights data (you can access yours from your profile):

I've been almost exclusively using the auto-matching feature, and as you can see from the 'Number of games' count, you tend to almost entirely get matched agains the similar-rated players. Sadly, no one uses the lobby, so to gain access to those gatekept strong players, you basically have to play tournaments. It's somewhat understandable that the stronger players are gatekept, because lower-rated players probably cheat more often. You can also see that I gain more rating against stronger players, which is another reason to play tournaments.

One last tip — don't let a strong tournament player guilt trip you into resigning. Their reasoning is that if it's a lost game, you should resign so that you can just move on to the next game and get a higher tournament score. But what they may not understand is, you can fight them to the bitter end to grab their rating points. If you're underrated, then why not?