The Olympus LM3 flash is the nifty little upgrade from LM2 flash that was bundled with the original OM-D EM-5. The LM2 really was an awkward flash, I (and I’d imagine most other photogs) would rarely bring it along because you can’t really diffuse the light, nor could you bounce it like you could with the (hidden) built-in flash on the Panasonic GX1 and Gx7. If I really needed more power, I’d opt for a compact TTL flash like the Nissin i40 and bring along a diffuser (Flashbender is my personal favorite). The LM3 flash was a little game changer bundled with the EM-5 II that allowed 90° tilt upwards and rotate 180° thus making it capable of bounce shooting! Though not very powerful with a guide number ~9 (a power measurement where entry levels tend to start at 36), it’s perfect for bouncing off walls and ceilings in most homes. For example, If we’re shooting at F2.8 at ISO100 with a GN of 9… 9/2.8 = 3.2M or just about 10 feet… and that doubles to 20ft at ISO 200, which is essentially the base ISO on most Olympus cameras (The “ISO low” feature overexposes the image and brings it back down to simulate lower ISO levels).
The LM3 could be such a useful flash, though on Amazon ($75) it notes that it’s only compatible with the EM5-II, presumably because the EM5-II added an extra port on the hotshoe to pass power to the flash. But good news, user “uberzone” on DPReview noted that the LM3 flash did work on his Panasonic GM5, which would be a really good small combo. The thread notes that it should work with any camera that includes this extra port on the hotshoe, which would be the Panasonic LX100, GM5 and EM5-II. Some users reported inconsistency on the LX100, which may be due to the LM3 flash being about 1mm bigger as the OP notes.
If you’re looking for a more powerful, yet still compact alternative, checkout the Nissin di466 which runs for about $140 (vs $75 for the LM3). It’s almost 4x stronger with a guide number of 33, and is wireless compatible. And it’s battery operated, which means it doesn’t suck your camera battery. Plus, it’s compatible with most diffusers designed for standard flashes. The Nissin i40 is another option (though a little more at $200), that features full manual control and High Speed Sync (HSS).