SupCom.log
I'm not sure how useful this is, the file was last modified several weeks ago. I just played a game in the steam client (and one on ForgedAlliance.exe for good measure), but it doesn't seem to log anything.

@jip
I downloaded the mod, but haven't enabled it yet. So far I've just been using the d3d_WindowsCursor command. The lag I'm talking about happens even when I'm not moving the mouse, and it started before I updated to an Nvidia driver with that issue. (I am getting cursor lag now though, which is why I use d3d_WindowsCursor, which fixes it. Cursor lag is different though, as it is much more severe and causes decreased frame rate. When I get a lag spike, it just causes all unit and particle animations to freeze in place for a fraction of a second, without decreasing the displayed frame rate.)

So I've been trying to get logs of a game, which is when I noticed that this lag only occurs when I don't play through the faforever client...
I have been playing offline so far by running ForgedAlliance.exe (under ProgramData\FAForever\bin) directly. What's weird is that I also get lag when I play Forged Alliance through Steam.
I assume the faf client is setting some parameters during startup that improve performance somehow? I haven't been able to get logging to work when I launch ForgedAlliance.exe offline, so I sadly can't provide a logfile that would show what the problem is. But I will just launch solo games through the faf client for now, since that seems to fix the problem.
A big thanks to you two for your help. If you still want to find out what causes this, I would be willing to provide a log if you tell me how to enable logging, but you don't need to go to any trouble for my sake.

Thank you for answering!
I'm using an Aspire VN7-793G that I upgraded with additional RAM and an SSD.
CPU Intel i7-7700HQ (4 Cores at 2.8 to ~3.5 GHz)
GPU Nvidia Geforce GTX 1060
SSD 960 EVO 500GB
RAM 32GB

I know that Notebooks make you think of overheating, but I am mindful of that, and the lag happens right from the start of the game, so I am pretty sure that it's not a heating issue.

I have an Issue with lag spikes that happen randomly and don't seem to be due to any of the well known possible causes. I linked a video that shows what I mean.
video
I don't see how this can be due to performance issues, since it happens with only a single unit on the map and regardless of graphics settings. I do have an nvidia graphics card, but this already happened before any of the driver versions that have known issues. (I did upgrade to the newest driver yesterday, in case that fixed the problem. I believe I was on 454 before.)
I have already spent several hours looking for a fix, but I haven't made any progress. I don't expect anyone will be able to tell what the problem is from just this, but can someone give me any advice on where to look for a solution?