In Scheme there's a let loop construct which is essentially the same as creating a self-recursive lambda in-place (aka 'named let'). For example, a factorial of 6 can be written as:
(let fact ([x 6])
(if (< 1 x)
(* x (fact (- x 1)))
x))
The question is: is there any alternative in elisp. And if there exists one, does it perform tail recursion optimization where possible?
You're looking for cl-labels. See https://stackoverflow.com/a/39564067/324105 for a very similar example to your code (along with some other related facilities).
See also: C-hig (cl)Function Bindings
does it perform tail recursion optimization where possible?
No, there is no TCO in Emacs Lisp, other than in the work-in-progress native-compilation feature (where it is currently disabled by default, so presumably not considered ready for general use; but even if it were, it would be a risk to rely upon it other than for personal use, as it's not safe to assume that other people will also be running native-compiled code).
For this reason, arbitrary recursion is generally eschewed by elisp programmers in favour of iterative techniques.