FATAL ERROR lock file "postmaster.pid" already exists

I add here what worked for me, after a long time of searching:

1. Delete the postmaster.pid file:

   rm /usr/local/var/postgres/postmaster.pid

2. Restart your postgres:

   brew services restart postgresql

Hope this helps someone ...

Update 8/2022:

As Mike commented, for M1 Mac you would replace stage 1 with:

rm /opt/homebrew/var/postgresql/postmaster.pid

Posting this in case it helps someone else:

I was having this same problem as the OP after a hard reboot when my laptop crashed. What helped me was running the following command to see what PID was associated with postmaster.pid:

cat /usr/local/var/postgres/postmaster.pid

The first number that appears will be the PID. Looking in Activity Monitor, I was able to see that Postgres was running, but without a PID number that matched the one shown.

Instead of the steps outlined in the answer referenced on Superuser, I restarted my laptop properly and then opened up Terminal and ran

brew services restart postgresql

This worked without having to remove postmaster.pid, which I saw a few other posts recommend. Sometimes it's the simple solutions that work.