Given the new log, it appears your computer definitely has a problem: this time your game crashed before the point it previously did. So it's not like there is one specific action your computer dislike for some reason, it's more like your game tend to crash for no reason, which is a very bad sign and not something I can prevent.
I can give you advices regarding your computer though: if you live in the northern hemisphere, we're in summer and it's not uncommon to see PC overheating. If you have any temperature monitor, look at it and see if everything is fine. If it's too hot or if you have no temperature monitor, it may be the time you open your computer case and remove all that dust (on all air exits, below the CPU fan - you need to unmount it -, etc). Beware that opening the case it can void your warranty if it's still relevant (not on the pieces itself though but it does matter for brands like Dell). This kind of cleaning makes miracles sometimes. If it does not change anything, though, I would like to suggest you to download a software to test your ram, then another one to test your CPU (CPU-Z may have both tests, I do not remember), and lastly another one for your GPU (some 3D benchmark for example).
On a sidenote, LUA is a programming language and it's the one that has been chosen by Firaxis. Mods typically have three elements: XML gameplay definitions (data like unit's name, strength, terrain's yields, texts, ...), XML UI definition (button at X=54, Y=103, image at...) and the LUA files to glue all of that and implements the mod's logic ("when user clicks that, do that"). All of those files are text files and you can open them with the notepad. LUA is not required for all mods (no need to program anything if you just want to add a building or a regular unit for example), but a mod like IGE is mostly about LUA for example.
Now, the LUA log is the output where things are written anytime I put a "print" instruction. It allows me to understand at which point of my code the crash happened, since I can infere from this log that it stopped somewhere between print("blah blah") and print("blah blah 2"). If error occurs ("such variable did not have any value"), civ5 also writes them in this log. If you wish to learn programming, LUA may be quite a good language for that (at least it was designed for that purpose) and programming is both very interesting and something you can learn alone, although the first steps are quite hard to do.
