Can type information be encoded in the untyped lambda calculus?
As mentioned in the comments, it is possible to reduce simply typed lambda calculus to untyped lambda calculus. This is the approach associated with Alonzo Church, called "Church Types" or "intrinsic types". Here, types are embedded in the language, and are intrinsic to the language. Still, the language can be stripped of it's types. 

However, it is also possible to construct simply typed lambda calculus from untyped lambda calculus. This approach is associated with Haskell Curry, called "Curry Types" or "extrinsic types". Here, types can be derived from the AST of the language.

The latter type is what you are looking for. A thorough overview of the subject is here