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

This error message indicates that the MySQL client is unable to connect to the MySQL server using the Unix socket file '/var/lib/mysql/mysql.sock'. There are several possible reasons for this error, including:

1. The MySQL server is not running: Check that the MySQL server is running by typing "service mysql status" or "systemctl status mysql" on the command line. If the server is not running, start it using the "service mysql start" or "systemctl start mysql" command.

2. The MySQL server is running on a different socket file: Check the MySQL configuration file (usually located at /etc/my.cnf or /etc/mysql/my.cnf) and look for the "socket" option. If this option is set to a different socket file than the one specified in the error message, update the socket file path in the error message accordingly.

3. The MySQL socket file is missing or corrupted: Check that the socket file '/var/lib/mysql/mysql.sock' exists and has the correct permissions. If the file is missing or corrupted, try restarting the MySQL server to recreate it.

4. The MySQL client is using the wrong socket file: Check that the MySQL client is using the correct socket file by specifying the "--socket" option when connecting to the server. For example, "mysql --socket=/var/lib/mysql/mysql.sock" would connect to the server using the socket file specified in the error message.

5. The MySQL server is not configured to use a Unix socket: Check the MySQL configuration file and look for the "bind-address" option. If this option is set to an IP address or hostname instead of "127.0.0.1" or "localhost", the server may not be configured to use a Unix socket. In this case, try connecting using the IP address or hostname instead of the socket file.