How to loop in a loopless language (Y Combinator)

In lambda calculus, you need recursion to do looping, and this is done using the Y Combinator formula.
Lambda Calculus Video: https://youtu.be/m32kbFXBRR0

For those unaware, lambda calculus is a turing complete programming language invented before computers ever existed. It is extremely simple and has an esoteric feel while having been invented as a serious mathematical model.