Attempt to display site authors in a carousel – User Image not Outputting inside li tags

You should be using get_users() – this will perform your query and also allow you to limit by role.

http://codex.wordpress.org/Function_Reference/get_users

userphoto isn’t a WordPress function, but get_avatar() is:
http://codex.wordpress.org/Function_Reference/get_avatar

Just check out the Codex examples and you should be able to modify to suit your needs!

UPDATE
I reread and realized maybe userphoto is coming from another plugin – yes? If so, check if the result of that function echos the result. If so, you will need to change that part to:

echo '<li class="author" id="author-'.$author->ID.'">';
userphoto($author->ID);
echo '</li>';