So I'm pretty lucky, I've had this laptop since 2018 and it's still working pretty well and pretty high speed even though I don't clean up my hard drive at all and stopped running antivirus because my pirated copy of Emsisoft (was the best anti-virus a few years ago, no idea how if fares now). If you can get one used and want a light laptop, these things are fantastic. The slimmest and lightest laptop I knew back then with both upgradable RAM and SSD. If I ever have to buy a "new" laptop, I'll probably just get a used/refurbished LG gram, I absolutely love this thing.
However, recently,
Hopefully this is helpful!
https://www.ifixit.com/Answers/View/564601/How+to+fix+the+hinges+on+LG+Gram+15.6%22
ugh yeah I've been there. Some particularly kind brands put the specs of the screw on the inside of the casing next to each screw hole (I've seen it on one HP but no idea about LG). it will probably be metric, something like M2, M2.5, M3 (if the screw heads were that small perhaps the smaller end of that list), but getting it just right, or getting the length at all, will be annoying unless someone else with the same laptop online has the specs or will measure for you
I guess you could take the screw out of the opposite side hinge and measure it, though it's not super easy to tell at these smaller sizes without specific tools like calipers or thread gauges
Does it sound like there might be anything else rattling around in there? In my experience repairing laptops a lot of times when the hinge would come loose like that its that the plastic housing of the brass inserts (where the screws are attached) has broken. Its usually pretty difficult to repair at that point, at least without having to replace whatever part its attached to.
This guide isn't specific to the LG Gram, but it give a general idea of what the repair might entail: https://www.instructables.com/Laptop-Hinge-Repair-Brass-Insert-Reattachment/
No, surprisingly no rattling. If I put it back in place with the screw from the bottom with my finger, it would behave fine. But some plastic housing could definitely be broken, I know two screws fell out and I can only account for 1