I need to pass UF wire through a 3/8" wooden shed wall. Can I use a LB
conduit body to accomplish this?

http://i1.quinbyhardware.com/6556641.jpg

There will be no conduit inside or outside the shed, just the UF wire.
The area where the body will be mounted is protected by a wooden fence
with about a 4" gap between the shed and the fence.

The plan would be to bolt the conduit body to the outside 3/8" of the
shed wall with the rounded bolt head inside the body and the washer/nut
inside the shed. I would use silicon sealant around both the bolt hole
and the hole for the LB body. The wire would be pulled up into the body
from below.

A quick test shows that the conduit body "sleeve" will extend past the
inside surface of the wall material by a small amount.