Currently, ob-lisp expects a package as a header argument. This is
inconvenient and often unnecessary. Slime (or sly) provides a function to
determine the current package: slime-current-package (sly-current-package).
The function used to do the evaluation in lisp is slime-eval (sly-eval) and
this function takes a second argument which is the package.

The current code determining the package is (in org-babel-execute:lisp),
(cdr (assq :package params)). As I understand it, on entry to
org-babel-execute:lisp, the current buffer is the org buffer, and the point
is at the beginning of the #+begin_src line. slime/sly-current-package
works just fine in that context.

I propose that the package determination be changed to

(or (cdr (assq :package params)) (funcall org-babel-lisp-package-fn))

with org-babel-lisp-package-fn being bound analogous to how
org-babel-lisp-eval-function is:

 (require (pcase org-babel-lisp-package-fn
    (`slime-current-package  'slime)
    (`sly-current-pacakge 'sly)))

This (approximately) seems to work fine in my emacs. However, I am using an
older version of emacs/org-mode and so am not submitted a patch, which
would be against slightly different code.

Regards,
Alan