parametrized function definition

[Joe Bloggs <who@cares.invalid>]

Hi, I am trying to write a function that allows me to quickly bind a key combination
to insert arbitrary text:

(defun set-local-key-insert ()
  "set a local key to insert some text"
  (interactive)
  (let (keystring textinsert) 
    (setq keystring (read-key-sequence "Key combination to bind: "))
    (setq textinsert (read-string "Text to insert: "))
    (local-set-key (read-kbd-macro keystring) (lambda () (interactive) (insert textinsert)))
    )
  )

However, this doesn't work since textinsert is not evaluated until the function is called with the keybinding. How can I get this to work properly? I am new to elisp so I imagine it's very simple.

Thanks.