Solved: ERROR 2002 (HY000): Can’t connect to local MySQL server through socket ‘/var/lib/mysql/mysql.sock’ (2)

I ran into this error on a RHEL machine that recently patched.  To correct the issue, I recreated the symlink in /tmp :

ln -s /var/lib/mysql/mysql.sock /tmp/mysql.sock
service mysqld restart

I found the solve and associated troubleshooting steps here: http://forums.cpanel.net/f354/cant-connect-local-mysql-server-through-socket-var-lib-mysql-mysql-sock-111-a-78444.html