lambda inside a let or letrec

[bolega]

My apologies in advance to comp.lang.scheme and comp.lang.lisp.

I am trying to run a certain syntax inside emacs lisp.

I know basically how let works

(let (list of pairs of var value) (function))

This is like a lambda function call , only the order is different.

But the novelty i saw reading a book on common lisp or scheme is this
and i failed to run in emacs. plz tell what modifications are needed
and i know they are different.

(   (lambda (n) (+ 1 n)) 3)  ;;; works in emacs

(let
((a (lambda (n) (+ 1 n))) (b 3)) (a b))   ;;; does NOT work in emacs

basically we are trying to use / abuse the let in that in the pair we
define a equal to a lambda. Then another pair where a value of b is
defined.

next, we want a to operate on b.

Why does it fail ?

The scheme/lisp book/paper where it was seen (forgot) used letrec.

Can someone enlighten me how set! and let can be used to formulate
recursion when the let has no recursion built in it ?

thanks a lot.
cheers