Of course I can, much faster. Maybe you do not see how high level the λ-calculus is... take a look on the Caramel syntax. I can translate line-by-line any Haskell program to Caramel. The λ-calculus, when given a decent syntax, is just Haskell without the types (but still has algebraic data structures identically, just no annotations). And I can be much more productive in Haskell than in Scheme, I think that goes without saying.

About the performance of the program itself, yes, λcalculus is faster than Scheme, by an order of magnitude, sometimes. For one, algorithms on church-encoded lists fuse by reduction, which means that the code below, in Caramel:

    map f (filter cond (zipWith (+) (map f a) (map f b)))

fuses to a single tight loop - i.e., it iterates through the lists `a` and `b` only once, and returns the result after that, creating no intermediate structure. Scheme would create 4 intermediate structures on this case. Since it is already 2~3x slower than the λ-calculus (running on GHC), that'd make it an order of magnitude slower in that case.