“Nedre” does mean lower (think cognate with Nederland). I’m not sure what gotten would mean. I’m guessing you’re think Got = God in German, but it’s Gud Norwegian.
Just to add to the above - Nedre or Øvre/Over (nether/lower or upper) is usually affixed to placenames to indicate old farms that have been split in two. Most likely the surname is derived from a farm or homestead named Gotten (maybe by the lake, maybe someplace else), that at one point in time was split into upper and lower Gotten. Hence the name.
As for Gotten itself - it could maybe be derived from Swedish - Gøta (Goth) is a common name for both parts of Sweden and the tribes that originated there - but who knows
Nedre does indeed mean Lower, and occurs frequently when farms have been split (but there is, apparently, no corresponding Øvregotten). According to O. Rygh’s Norske GaardnavneGotten comes from gata ‘road’ - it’s possibly a definite dative plural form. (Incidentally, in Old Norse, ‘god’ was goð or guð, and ð generally became d in modern Norwegian, not t or tt.)