Annexe (4-2)
(Other definitions for lean-to that I've seen before include "Shed, outbuilding" , "Attached outbuilding" , "Building with roof resting against larger building (4, 2)" , "Small building resting on side of larger one" , "Penthouse" .)
'annexe' is the definition.
(synonyms)
This is the entire clue.
(Other definitions for extension that I've seen before include "Annexe" , "Added part" , "Office phone, perhaps" , "supplement" , "new part of home?" .)
'annexe' is the definition.
(synonyms)
This is all the clue.
(Other definitions for wing that I've seen before include "Stage area out of sight of the audience" , "Pinion" , "Organ of flight" , "Aircraft lift provider" , "Flank; move quickly" .)
(Other definitions for leanto that I've seen before include "Roof" , "shed" .)