I have chased electric gremlins in my cars before. Thankfully, never really had to do that with the LX much. So these are just random things to look out for (not related to the platform specifically).
- What is on your keychain? any magnets, any other door key chips. e.g a gym key that you touch on a scanner to unlock the door etc.
- Look for anything done to the wiring, anything out of place. Any splices, maybe some previous work (before you bought the car) that was done for whatever reason. Especially soldering, never ages well for joining wires. You might have to pull some of the interior panels to inspect the wiring that goes to the key switch and trace it back.
- Have you tried using a different master key? Also open the key fob see what it's looking like. I have one Ebay master key and it's remote is separate from the small rice grain sized chip that servers as the ID for the key. If its moving around in there it might cause weird issues.