Video desyncs with the audio over time I record footage with OBS and do voiceovers recorded in audacity. I process the audio in audacity, then sync the audio with the video. However, since I started doing it this way, the audio and video are not syncing up.

It starts out fine with a definite sync point (countdown from 3 and then I do something like click on something) but as the video progresses, the video starts lagging behind the audio. near the end of a 20 minute video, the disparity is nearly 3 seconds.

Someone brought up framerate. the footage is 30 FPS and Lightworks lists the audio as 24 FPS. The mic is set to 44100 Hz as well, if that helps.
Make sure the sample rates in both systems are the same. I don't know what OBS is, but if I was using Final Cut for video editing, I would make my project 48kHz, and make sure any external recordings were also at 48kHz. Even with the same sample rates, audio will drift over periods of more than a few minutes. Either sync it up manually in chunks, or use something like Pluralize to do it for you. (Or have a fixed sample clock  between all your devices when you record- probably not possible)