Martin, while others may have still more to say, I’ll chime in with more to consider/try. It’s not brief, but it’s how I would approach this if it happened to me:
- I’d wonder if you tried downgrading back to 5.3.10.97, since all this started for you when you went from that to 5.3.10.120. I’m not saying you SHOULD have to, but if you did and things worked, it would confirm that’s the problem.
Conversely, if it does NOT fix things, then I’d be wondering if that first update failed in some way, leaving things botched–and in such a way that the downgrade would not “repair”. Same with the prior steps today of dropping in the jar.
- If things still fail after that, I’d recommend trying to uninstall Lucee (given you did the prior steps Andreas offered today), then reinstall.
If that goes well, does your site work locally as expected? If not, it would suggest some bigger problem, right? But if the local site DOES work, try the Lucee admin update again. If I things works after that, it was some cobweb that’s now been wiped clean, and not likely even worth pursuing further, I’d think.
FWIW, there’s zero reference to that error in withe the lucee forums here or the broader web. That’s an indication of how unique this problem is. If it ever happens to anyone again, perhaps they may find this and add an update if some new info is found be then. 
- Finally, if you may say you DID try reinstalling and the local site fails immediately, you may feel stuck. But you could consider repeating your initial steps on a different machine or VM (or the Windows Sanbox on THIS machine), to see if all works–the install, the local site, the update.
If they did, then at least you’d Know now that there’s something other than Lucee that’s somehow gone amiss on this current machine.
- And to that point, or if you don’t want to try steps 2 or 3 (my step 1 seems trivial to at least try), my next guess would be something in the iis configuration - - since the url of your failing local request shows you using no port, I’m assuming that’s going through iis. Clearing out iis settings can be a challenge: the configuration elements could be at the iis site level (perhaps in the web.config for the site) or at the iis server level (in the applicationhost.config, which csn hold site-level config as well).
Lastly you say all was working initially (remote and local requests via iis to Lucee), so I’ll assume you’re not serving the local and remote requests via different iis site configurations somehow, as that could add more challenge “cleaning things up”.
But I realize you may not want to “go there” yet (about considering iis config issues), so I’m just
planting that seed, for you or others.
Let us know if you try/learn anything.