The error message “Can’t connect to local MySQL server through socket ‘/var/lib/mysql/mysql.sock'” typically indicates that the MySQL server is either not running, or it is configured to use a different socket file than the one specified. To resolve this, first ensure that the MySQL service is actually running. You can check this by executing `systemctl status mysql` or `service mysql status`, depending on your system’s initialization system. If it’s not running, start the service using `systemctl start mysql` or `service mysql start`. If it is indeed running but you are still facing this issue, you may want to check the MySQL configuration file (typically found at `/etc/my.cnf` or `/etc/mysql/my.cnf`) to verify the socket path specified under the `[mysqld]` section, and ensure it corresponds to the actual socket file in the specified directory.

Another common issue that can cause this error is permissions related to the socket file’s parent directory. Make sure that the MySQL server has the necessary permissions to create and access the socket file in the specified path. You can check the ownership of the `/var/lib/mysql` directory using `ls -ld /var/lib/mysql`. If the ownership does not correspond to the MySQL user (commonly `mysql`), you can change it with `chown -R mysql:mysql /var/lib/mysql`. Additionally, the `mysql.sock` file could also be absent if MySQL crashed or was not properly shut down. In such cases, check the MySQL error log usually found in `/var/log/mysql/error.log` or `/var/lib/mysql/[hostname].err` to identify any startup issues causing the socket to fail creation.