Keys can only be bound to commands.
A command is (usually) a function which contains an interactive form. This form must be included even if your function takes no arguments.
Hence:
(global-set-key (kbd "C-x 8 l") (lambda () (interactive) (insert "λ")))
In addition, keyboard macros are also commands, and can therefore similarly be bound to keys.
"λ" is a valid keyboard macro for inserting a lambda character, and so (as per Dan's comment above) the following also works:
(global-set-key (kbd "C-x 8 l") "λ")
See also:
- C-hig
(elisp) Defining CommandsRET - What is the difference between a function and a command?