Unfortunately, for whatever reason, as you have discovered, LR does not have a pull-down selection of RAW development profiles that are equivalent to the native in-camera profiles for Panasonics. They have them for Oly, they have them for Sony....but not Panasonic.
You can pretty easily create your own if you have a color calibration card/chart, by photographing the card in the light you will be using, and then adjusting the color/hue/luminosity sliders to match the card colors to the JPG version. It takes a little practice, but you can come up with some pretty good profiles if you work on it.
I had to do this with the GM5 as its RAW output in LR is just dreadful. I came up with a good profile for it for very bright shooting situations that I use when doing outdoor sunny day flower photography, and it works quite well.
I did also, however, purchase a set of Huelight profiles for the GM5, and those are very good, especially for more normally lit images. They are vastly superior to the LR6 native conversion profile, and can be used as is or as starting point for developing other profiles, too.
Interestingly enough, I did pick up an X-Rite Color Checker Passport a number of years ago, when I had a GH2 (which had some major color rendition flaws that needed addressing). It includes a handy white balance and color card in a protective plastic case, plus software to analyze the images you take of the card and generate profiles automatically. The card part of it is really nice, as it's very handy and nicely protected when you take it with you. However, I don't think the software has really kept up with newer cameras. It generated very good profiles for my GH2, but on every more recent camera I've used it on, it has heavily oversaturated the reds, and I've had to do major adjustments to whatever profiles it has ended up auto-generating. So, now I use the card as a starting point and then do a manual profile if I need one (with varying degrees of success ) As a result of this experience, I think you probably could do just as well with a good set of the color cards alone, and manual adjustment to generate a good profile.
The other thing you could do is change your workflow a bit. You could open up the RAWs in SilkyPix, which is supplied by Panasonic, and, of course, DOES have the profiles loaded, and then export a TIFF or DNG file with the native profile applied, and then work on that in LR, instead. It would definitely give you access to the native profile as a starting point for your RAW development, even though it's a bit of a pain to do it that way.
Hope this helps,
-J