$ sudo apt-get update
$ sudo apt-get install libqt4-sql-sqlite 

libqt4-sql-sqlite is installed in your system.

Make ensure the libqt4-sql-sqlite package were installed using the commands given below,

$ sudo dpkg-query -l | grep libqt4-sql-sqlite *

You will get with libqt4-sql-sqlite package name, version, architecture and description in a table

libqt4-sql-sqlite package basic information: