MongoDB: exception in initAndListen: 20 Attempted to create a lock file on a read-only directory:...

The problem is that the directory you created, /data/db is owned by and only writable by the root user, but you are running mongod as yourself. There are several ways to resolve this, but ultimately, you must give the directory in question the right permissions. If this is for production, I would advise you to check the docs and think this over carefully -- you probably want to take special care.

However, if this is just for testing and you just need this to work and get on with it, you could try this, which will make the directory writable by everyone:

> sudo chmod -R go+w /data/db

or this, which will make the directory owned by you:

> sudo chown -R $USER /data/db