The GX7 was a fantastic camera when it was first released.
It still is.
It compares well and occasionally favorably with the camera which replaced it - the GX80/GX85 - which although an upgrade in certain areas, was a downgrade in others.
The other huge plus about the GX7 is that its prices have dropped - which makes it one of the more affordable members of the Lumix family of mirrorless micro 4/3 interchangeable lens cameras.
The biggest improvment over your LX7 - which incidentally is still a fine camera - a great portable travel camera - and has superb close-up/Macro capabilities - is not only in the larger sensor size (giving you better IQ, better dramatic range, better ISO sensitivity, better everything) but in fact the GX7 had a much improved m43 sensor for the time which still is almost state-of-the-art.
Keeping the LX7 will give you 2 great cameras, btw. With regards to your questions about the differences between the 2 similar models of the kit zoom, I honestly don't know. I've had excellent and superb results from a 14-42 II Panasonic, can't remember which one. Also, to echo the comments of several other posters, the tiny 12-32mm pancake lens is astoundingly sharp - more than the equal of the larger 14-42 models - and has the advantage of making your whole camera + lens combo feel almost tiny.
One last point - or question ---- given the seriously improved image-making nature of the GX7 & its sensor over the tinier, older, and just not-quite-as-good (though still capable) LX7 --- have you considered buying a good all purpose prime lens, instead of a zoom, for the GX7? If not, perhaps you should. Certain prime lenses give demonstrably better results and performance than most of the kit zooms. Additionally, some - like the diminutive but wonderful 20mm Panasonic pancake lens (both in its 1st generation version and the newer version) are both affordable and amazing. Additionally primes tend to have lower f/stops i.e. wider apertures - that is, they are better suited for lower light shooting - for bokeh - for many things, actually. The 20mm (the equivalent of a 40mm traditional 35mm FOV, halfway between a very wide 28mm and a more standard-wide-classic 35mm FOV) is both great and very affordable. The Olympus 17mm f/1.8 (or is it f/1.7?) lens is another superb general purpose prime with remarkable optical qualities which many people keep parked semi-permanently on their micro four thirds bodies. Also the 25mm offerings from both Panasonic and Olympus are both affordable, extremely high quality, and low-light capable - making them intriguing competitors.
Bottom line - with the right prime on your (new or newer) GX7 body - I suspect you might be able to see seriously significant improvements in image quality -dynamic range - and many other subtle aspects of what makes some good photographs...great.
Good luck in your choices. But to repeat - the GX7 is a great camera - a good upgrade - and quite affordable these days.