What else was plugged into the circuit? As in, in your house/aparment/dwelling what other devices were plugged into electrical circuit that goes to your breaker. For instance all the wall outlets in one room may be on the same breaker circuit. It is my experience with electronics (electrical eng) that there are a multitude of reasons a device might blow. You say your lights were plugged into this outlet. They had only been on for 15minutes. Is there any kind of starter for these lights,(after startup maybe the starter overloaded in some way), is it possible for your lights to get wet(water got onto lights enough to cause some arcing interally that caused a high current pull which would have started to melt the plastic and thus possibly catch fire), Is there any salt creep interal to your lights kind of like same as above causing arcing issues), is the lighting cooled properly, are all the lighting ballast cooled properly(again if your lighting system overheated(seems unlikely from only 15 min on time though), how old is your lighting setup.... I Think you see what I am getting at. My experience with melted plugs alot of times is that the device plugging into the socket is the culprit.
Like I asked above is there anything else on this circuit. TV, stereo, ....? Did you turn on something else in house with heavy electrical draw. It is possible that maybe this circuit was close to fully loaded and when those lights came on it pushed it over the edge. Then it started to heat up from overdraw on the circuit and your lighting plug or RK2 was the weakest link and melted. The rating on the RK2 says 15A total from what I can see in the picture. I know a stupid question but whats the total current rating of all devices plugged the RK2. Also is the RK2 plugged into something else below it. I am not familar with the unit but it looks like maybe its plugging into a power strip?
GFCI did not trip -- This is totally possible. If there was a small interal arcing in a unit it might only cause the device to pull more current all the while heating up some interal piece of the unit....Also it is possible that some part of your lighting is not fully grounded(again this one is unlikely) and thus the GFCI would have not seen any current on ground line.
Maybe try replacing the plug on those lights and plug them in and see if they are still working and also inspect the lights themself. Maybe just electrical spike from outside, humidity, bad luck?
I just throwing out some food for thought. This just a starting list of things I would start to look at for the cause since the RK2 people didnt seem to have an answer for you
