First of all, let me qualify by saying that the shots were purely social shots (or record shots). The intent was to get properly exposed, technically good shots, rather than competition-quality shots (which is always difficult to do on a family event).
During this trip I had many opportunities to use the flashgun: a wedding dinner, inside a museum, just before sunrise and just after sunset, inside a batik factory, and an indoor social gathering. A high percentage of the shots were taken with the flash.
Here is my experience. The flash-aided shootings went as well as I imagined they would be, but could be improved. For one, I think I should have kept the ISO fixed at 80 (the lowest possible in the LX7). I used the P mode, which worked quite well. On hindsight, it wouldn't have hurt to keep it in M mode with speed setting of 1/60s and aperture wide open.
In the following, the wedding dinner image was at ISO 100, the sunset was at ISO 100, the factory hand was at ISO 400, and the museum was at ISO 80. All were shot at speed 1/60s, with Stofen diffuser fitted on flash.
In the wedding dinner scene, a large sensor high-ISO camera would have been better, especially since the presence of large mirrors actually created an annoying flare in some of the other images when the flash fired. This LX7/flash combo worked alright, but only just. In the other scenes, I did not miss having my Nikon D700 with me, as the tiny LX7 was a joy to carry around (although not the fairly large flash gun). I did get a few looks from other photographers at the wedding, as I must have looked odd holding the LX7 on one hand, and the flash on the other.