How to reinitialise /var/lib/mysql files? Due to a mishap I deleted the entire /var/lib/mysql directory. Since the database did not contain anything important, I do not want to go through the hassle of restoring it from an old backup, but instead create the directory structure from scratch. How do I do it without reinstalling MySQL?
You should be able to just run mysql_install_db from the command line

mysql_install_db initializes the MySQL data directory and creates the system tables that it contains, if they do not exist. It also initializes the system tablespace and related data structures needed to manage InnoDB tables. As of MySQL 5.6.8, mysql_install_db is a Perl script and can be used on any system with Perl installed. Before 5.6.8, it is a shell script and is available only on Unix platforms.

Please read the MySQL Documentation in full for mysql_install_db, then ...
GIVE IT A TRY !!!
If it does not work on the first try, do this
mkdir /var/lib/mysql
mkdir /var/lib/mysql/mysql
chown -R mysql:mysql /var/lib/mysql 

then run mysql_install_db again