You can install an rpm with an ignore dependencies switch. But, you will still run into problems down the road in Synaptic package manager with missing dependencies. I think you got into a spot of trouble early on when you started adding packages without first installing apt-sources-list. The upgraded repository list is necessary because a few repositories dropped support for PCLinuxOS updates. As a result, you started with an outdated dependency chain.
How far are you into this LXDE install?
EDIT: It would probably take you less time and effort to reinstall than to troubleshoot. Especially if you don't know what to look for and what to do with what you find. If you were to reinstall, it would be a pretty quick procedure. But, you'd have to do things in a certain order.
1. Reinstall LXDE.
2. After first login to the new installation, open Synaptic. Click the Reload button. Do not install any extra packages, except for the apt-sources-list package. Only that one package. Click the Apply button to install that package.
3. No need to close and reopen Synaptic after installing the apt-sources-list package. No need to reboot. Just choose a repository from your new repository list.
4. Click the Reload button again.
5. Do not install any extra packages.
6. Click the Mark All Upgrades button.
7. Click Apply.
8. After installing updates, if you are told to log out or reboot, do so before doing anything else.
9. Open Synaptic, if it's not already open. Click the Reload button again.
10. Click the Mark All Upgrades button again.
At this point, you will probably have nothing left to update. Before installing any new packages, always do your updates first. This is a general rule. Now you're ready to install extra packages.