Has it been raining where you are? The alarm on my car (not a Lexus) can go off repeatedly if a sensor gets wet. The trunk area appears to be the vulnerable spot for my car. A severe rain storm or car wash can set off. so can opening the trunk in moderate rain.
It could be that it's telling you it's a worthless relic and that even when going off no one would care if it was being vandalized...unless it was going off in the middle of the night, then the police would be called....to tow it away for being a nuisance.
Your car battery could be going dead-lots of weird electrical phenomena start happening when the voltage drops off.
After that, factory alarm or aftermarket alarm?
Factory alarms are good, generally, and aftermarket can be pieces of pure junk. A regular repair shop can fix the factory alarm, because the wiring will be in the manuals, and a troubleshooting guide. On the aftermarket, go to a shop that installs them, like Tint Specialists, and they can usually figure out what is wrong, or put a new one in.