There is very much an "if-statement" in lambda calculus.
The basic idea is, in the Church Booleans, we think of true as a function which takes a then clause and an else clause, and returns the then clause (T=\lambda xy.x), and false as a function which takes a then clause and an else clause and returns the else clause (F=\lambda x y.y). Then we get our if statement just by applying a predicate (which returns F or T) to a then clause and an else clause. Indeed, that is very much a way to get recursion to step -- the typical Church-numeral definition of the factorial function works that way.
By the way, one sure-fire way to get evaluation of a lambda expression to terminate if possible is leftmost-reduction -- that is, reducing the leftmost redex first. Intuitively, the leftmost redex is the "outermost," and any other reduction preserves it, so it must be reduced at some point.
The basic idea is, in the Church Booleans, we think of true as a function which takes a then clause and an else clause, and returns the then clause (T=\lambda xy.x), and false as a function which takes a then clause and an else clause and returns the else clause (F=\lambda x y.y). Then we get our if statement just by applying a predicate (which returns F or T) to a then clause and an else clause. Indeed, that is very much a way to get recursion to step -- the typical Church-numeral definition of the factorial function works that way.
By the way, one sure-fire way to get evaluation of a lambda expression to terminate if possible is leftmost-reduction -- that is, reducing the leftmost redex first. Intuitively, the leftmost redex is the "outermost," and any other reduction preserves it, so it must be reduced at some point.