Using Template Haskell instead of a parser.

THParser.hs

import qualified Language.Haskell.TH.Syntax as TH

data ULC = Var String | Lam String ULC | App ULC ULC deriving (Show, TH.Lift)

quote :: TH.Exp -> Maybe ULC
quote (TH.VarE v) = Just $ Var (TH.nameBase v)
quote (TH.UnboundVarE v) = Just $ Var (TH.nameBase v)
quote (TH.AppE x y) = App <$> quote x <*> quote y
quote (TH.LamE vs x) = foldr (\v xs -> Lam <$> (case v of TH.VarP v' -> Just (TH.nameBase v'); _ -> Nothing) <*> xs) (quote x) vs
quote _ = Nothing

q :: TH.Quote m => m TH.Exp -> m TH.Exp
q x = maybe (error "Unquotable expression") TH.lift . quote =<< x

-- >>> $(q[|\s z -> s (s z)|])
-- Lam "s" (Lam "z" (App (Var "s") (App (Var "s") (Var "z"))))