I can't make a claim for the Lucerne, but I've had issues with GM speaker wiring and speakers in the past, so I've got a few ideas:
1. Defective speakers. I have personally experienced my mom'* '99 Intrigue and my late stepmother'* '99 Alero both suffered failure of the speakers in the rear package shelf (6" x 9"). I've also seen the same thing happen in a '97 Malibu. I certainly hope GM dealt with Delco'* speaker division to address such prevalent failures in factory speakers, I've seen complete failure of the speaker (will not produce sound at all), or failure of one full speaker and partial failure of the other rear speaker (either intermittent operation, or loss of all sound below the highest of treble with intermittent woofer operation). So JWFirebird is definitely valid with swapping it out with the other side.
2. Corrosion/looseness of the connector would definitely be suspect, especially knowing the door in question has been recently worked on. If you pull the door panel off, make sure any internal plastic shielding that is glued onto the inner door frame (they do still do that, right?) and if GM built a plastic or cloth speaker baffle going behind the speaker are properly installed. This will help keep moisture exposure and corrosion to the connector at a minimum.
3. Completely unrelated wiring issue within the dash, specifically at the harness-to-stereo connection. A friend of mine'* '99 Alero (not my step mother'* car, simply a coincidence) had that specific problem, and my '94 Cavalier was NOTORIOUS for speaker dropouts at the harness connector (wiggly connections). The easiest way to fix this requires some up-close-and-personal time with a set of small metal picks. I've had to bend both the tiny retainer tabs on the individual wire connectors, and the connectors themselves to spread them out a little (then the connector is V-shaped) so make them connect more snugly.
Yeah, that wasn't very clear, but I'm not sure how to really explain it any better than that.
4. Impending failure of output channel(*) of factory stereo (or factory amplifier[*], if equipped). First, if you don't have external amplifiers (some premium sound systems have one, on others the speakers are driven directly by the deck), troubleshooting will be a little simpler. When it happens, check the same side speaker in the opposite location (check front/back, and front tweeters if you have them) to make sure that you're only losing ONE speaker. It can be hard to tell sometimes with the acoustics of the car if you've lost one whole channel (side).
This test won't be reliable necessarily if your setup has an external amplifier. If you want to know the whys, I can get deeper in another post.
Once you are positive it is one speaker, it'* MOST LIKELY not the stereo unit itself (typical setups have two amplification sections, left and right, which are blended in essentially another circuit for front and back). If it'* BOTH speakers, and you DON'T have factory amplifiers, then it is PROBABLY the stereo.
Oh - if your door/seat belt chime is piped through the front left speaker... I don't know if that interface has anything to do with it. I know absolutely nothing about those systems, and I'm a semi-pro at car stereo installation. LOL