They didn't. Pure lambda calculus would have been "a function that when applied to a number encoded as a function, extracts that value".

They did it essentially as a linked list, C-strings, or UTF-8 characters: "current data, and is there more (next pointer, non-null byte, continuation bit set)?" They also noted that it could have this semantics without necessarily following this implementation encoding, though that seems like a dodge to me; length-prefixed array is a perfectly fine primitive to have, and shouldn't be inferred from something that can map to it.