I think I would use something like Tyvek house wrap against that wall from inside the lean-to. It breaths but keeps moisture out.

I built mine exactly this way. My siding is the hardy plank. Of course without opening the wall I wont know if any moisture gets in but I will suggest that he puts a good bead of caulk around the outside frame and all should be good. Teds ideas of the Tyvek is a good one also.

Mike

Would a brick house need Tyvek?

For what it's worth.

My first greenhouse was a pit/leanto built onto the side of a garden shed. It was 8x12 and had a door leading into the shed. The moisture from the GH got into the shed and the drywall panels i used to finish the shed ceiling (was a nice shed!) all sagged like 3-4 inches! I might not have had that issue if I used greenboard but i don't know.

The shed was 12x12.

The point being, there is considerable moisture in the GH.

Note: I did use a rubber membrane along the south wall to prevent moisture from getting into the wall framing.

poppa-
Thanks for the info. Did the shed wall have any kind of tarpaper or other moisture barrier under the siding? Was it very moist inside the greenhouse? And did you heat the greenhouse?