So, I just wanted to thank you for this tip, and I really recommend that other people try this if they have problems with the game. I've been having some pretty severe lag for so long that I just got used to it, and it never crossed my mind that cleaning the inside of the computer would help.
But then I read this, bought a can of compressed air, and tried it. Now, I did run into some issues, because I was stupid and didn't pay much attention to the space below the graphics card, where there was a fan I didn't know about. When I was done cleaning and tried running the game, it ran SO smoothly, but then the computer turned itself off within a minute - the system log told me the graphics card overheated. Taking apart the computer again, I saw that there was a chunk of dust in the barely-visible fan, which probably prevented it from spinning. So yeah, real dumb. Should've seen that.
Anyway, having gotten rid of the dust, the game now runs so, so smoothly. Graphical settings were turned way low before, so I can probably even turn them up a bit now and still run the game better than I used to. So, thanks!