I'm flashing a new nightly version of LineageOS. I'm just gonna flash it without wiping data/system since I already have it installed. However, I also use Gapps (stock variant). Do I need to flash an updated version of it too?
You normally don't need to re-flash GApps as most GApps installers will install an
addon.d script which restores GApps automatically after flashing a new ROM that supports
addon.d (LineageOS does so).
If you are using Open GApps (http://opengapps.org/) you are on the safe side.
@timoschwarzer already described the persist function of (most) GAPPS packages, so I'd approach this from a different side:
You are still advised to update GAPPS from time to time (in orders of months), due to Google introducing new functions, APIs, etc. in updated versions of their apps, but not doing this usually doesn't affect working aspects of your device.
When you do it, make sure you do a nandroid backup prior to manually flashing the new GAPPS package, and test out updated apps that you often use to find out whether the change is to your taste, so that you could roll back if it turns out unsatisfactory or causing issues (e.g. Google App updates often cause battery drain).