Hello and Welcome to Ubuntu Forum
First thing first, please be advised that Lubuntu Software Center (LSC) is under development and as of today, there is no stable version.
Now, to install LSC, please do this:
sudo add-apt-repository ppa:lubuntu-desktop/ppas
To make sure LSC is still on your system, please open LXTerminal and type:
sudo apt-get install lubuntu-software-center
I personally don't like any software center, I just use the terminal and Synaptic when I have to. But that's me