It depends on the type system you choose to apply to LC. Simply-typed LC terminates. You have to include a construct that introduces general recursion to make

It depends on the type system you choose to apply to LC. Simply-typed LC terminates. You have to include a construct that introduces general recursion to make it Turing complete. There's a cool practical space within those constraints that needs more exploration. Non-total functions can call total functions, but not vice-versa. Imagine a web server whose main loop is non-total, because you want it to stay up. But each route is total, to guarantee termination.