The built-in speaker is no longer working

From what I can make out from the Owner’s Manual (ftp://ftp.panasonic.com/camera/om/dmc-lx...) and the Disassembly Guide (Panasonic LUMIX DMC-LX100 zerlegen) the speaker is in the bottom of the camera near the left hand edge. The last photo in the disassembly guide shows a multiway ribbon in that corner of the camera body, which presumably serves the speaker, but it has too many connections for that to be its only function. Maybe the WiFi module is hidden in there. The audio amplifier could well be in there as well, but that still doesn’t account for the number of connections. The first thing to try would be to reseat that ribbon in its socket, but if that’s the problem I would expect the WiFi to be no longer working.

In any case, your best bet is to find another camera of the same model on eBay offered as “spares or repair” and with a different fault (e.g. lens error). Older and non-functional digital cameras go pretty cheap. You can practice disassembling it and once you’ve mastered that you’ll have the skills and required spare part to fix your own!