I am looking for a way to combine two lambda expressions, without using an Expression.Invoke on either expression. I want to essentially build a new expression
Your solution seems to be narrowly tailored to your specific problem, which seems inflexible.
It seems to me that you could solve your problem straightforwardly enough through simple lambda substitution: replace instances of the parameter (or "free variable" as they call it in lambda calculus) with the body. (See Marc's answer for some code to do so.)
Since parameter in expression trees have referential identity rather than value identity there isn't even a need to alpha rename them.
That is, you have:
Expression> ab = a => f(a); // could be *any* expression using a
Expression> bc = b => g(b); // could be *any* expression using b
and you wish to produce the composition
Expression> ac = a => g(f(a)); // replace all b with f(a).
So take the body g(b), do a search-and-replace visitor looking for the ParameterExpression for b, and replace it with the body f(a) to give you the new body g(f(a)). Then make a new lambda with the parameter a that has that body.