Clx16The factory alarm is all plug and play.. in other words your LX was delivered to the US without an alarm. They only had to unplug some connectors and insert their own wiring hardness and that little box to give you an alarm. @Rusty Marlin 's instructions above tell you how to not bypass the factory alarm but take it back to its form when it was delivered to the US. That being said, since the factory alarm was "bypassed" by the aftermarket installer, in place of just removing it, I don't know where they spliced in and to what. It is a regular problem for all kinds of vehicles when vehicles have more than one security system. it adds points of failure... I don't remember the pin out but there is a jumper you can make for the plug under your seat to get you back started. I just am at work and can't search out the post for it at the moment. However below is a great reference regarding your alarm and wiring harness.
Disclaimer: this should work for any US spec 96 LX450 that has the factory installed RS3000 alarm, OTHER YEARS/MODELS MAY BE DIFFERENT, but this should still serve as a valuable guide. Do this mod at your own risk. Read through this guide and look at the pics before starting your install. I...forum.ih8mud.com
i would make sure you removed the factory alarm wiring harness before trying to troubleshoot the aftermarket device and the rest of the vehicle. If you can't do that, then find the post where someone shows you how to jumper the harness to get it started.