How did the bug get in there? Seems like there must be some bug-sized passage that would allow entry. . . Right?

You could try porinig some Isopropyl alcohol into the assembly, and seeing if you can get that bug occupied chamber to fill with the alchol. Then. . . Shake, Vigorously. Bug should separate into pieces and perhaps can be drained out with the alcohol. Allow the alcohol to drain completely and assist drying the interior of the lamp assembly by blowing (compressed or canned or blower) air into the assembly. This process may take a couple of applications to completely remove the bug. Allowing the assembly to dry completely between sessions will allow time for the alcohol to help "break apart" the bug, as the alcohol will dry the critter out.

Good luck removing this thing that is bugging you!