Given a λ-term, can I decide which machine model I need to express it?
Paraphrasing, this seems to be your question:


  Given an unrestricted λ-term, can I determine what kind of automaton/machine model I need to express it?


Such properties are inherently undecidable (usually).
Starting with a Turing-complete formalism, Rice's theorem immediately tells you that what you are asking is impossible.

The set of TMs/λ-terms corresponding to any non-empty, non-Turing-complete machine model forms a non-trivial index set and is thus is never decidable.

Of course, if you restrict yourself to a less than Turing-complete base set of terms, Rice's theorem does no longer apply. This is still a tough question to ask, though, even at lower levels of the hierarchy. For instance, it is undecidable if an NPDA accepts a DCFL, if a context-free grammar describes a regular language, or even if a context-free grammar is equivalent to a fixed regular grammar.