Problems with blocked players - Why are they allowed to watch my games and write comments to me?

It's not a matter of having a solution, it is against Lichess philosophy. By this philosophy users should not have the ability to ban other users from public events or deny them access to view chess games (Lichess being an open source projects which supports free sharing of information).
As was mentioned several times, harassment would have a separate treatment.

They were watching my games after I blocked them, and some comments were made in the game chat and also public arena chat to try to communicate with me, despite me saying clearly that I didn't want to talk to them.

Please report the player via https://lichess.org/report

@VelociraptorRex said in #13:

We need some kind of personal shadowban then: let's say player X which has player Y in the blocklist won't see any comments from player Y or his spectating.
Thus the player Y rights won't be broken as well as mental health of player X.

This is a good solution.