lubuntu-software-center binary package in Ubuntu Trusty amd64

 The Lubuntu Software Center lets you browse and install thousands of
 applications available for Lubuntu. You can view available
 applications by category, or search quickly by name or description.
 You can also examine the applications already installed, and remove
 those you no longer need.
 .
 This center was especially optimised for Lubuntu, but you have access to the
 same free applications than on Ubuntu Software Center.
 .
 To install or remove software using the Center, you need administrator
 access on the computer.

Source package