Thanks, all. Sorry I didn't mention my OS, originally. My PC is, in fact, running Windows. As for the card getting close to burn out, I monitor my temperatures compulsively and do a fairly thorough cleaning of the inside of my PC about once a month. My most recent cleaning was only a few weeks back, but I did go back in for another round today. Figured it couldn't hurt, especially since the GPU fan is in a bit of a hard to reach spot, and it was possible I missed some dust.
Anyway, it was no dustier than what you'd expect after a couple of weeks of accumulation. Really pretty decent. Temperatures (according to both MSI afterburner and SpeedFan) remain nominal. In fact, because it's winter, they are actually below average for a relatively clean interior.
I then decided to see if any similar crashed would occur when I tried to play a commercially released game. Probably the most "advanced" game I've got is Thief (the new one), which I already own on the PS4 but had picked up at a Steam sale specifically to see how my PC performs with what's considered "next" (or now current) gen graphics. It's definitely not a game I can or should run at absolute highest settings, but I did try, just for a sort of stress test. While it is basically a slideshow where FPS is concerned, it does actually run, with no crashes. With a few tweaks to the settings (turned off anisotropic filtering and tesselation, switched textures from very high to high, kept shadows and light same), the game began to run pretty well (about as well as the PS4 version), with occasional stuttering, but generally an average framerate of 50 fps. I played about an hour and a half with no issues, temperatures remaining well within expected range.
I then started up lightwerks again, turned all setting fairly low (just to see if that was contributing to it), loaded up a simple scene with two point lights within reasonable distance of one another, had a crash (and Error code 7) within moments. I can reproduce this reliably with pretty much any scene with lights that overlap even a little bit. It's not specific to a particular map...again, Graphics card is relatively clean, relatively dust free, is not running hot, and plays recently released games that make heavy use of lights and shadow, as well all sorts of moving parts, without any unusual trouble...
UPDATE: Okay, now I feel silly. My apologies. At least for this most recent test, it would appear that I had the anisotropic filtering in the editor set to something ungodly and astronomical...which I suspect was a slip of the finger, since I usually keep that setting down in most games. After fixing this, I am not getting similar issues. That may well have been the problem.