Is the className on the <li> element? If so, you could do this:
$('#container ul li.' + className)...
You're just concatenating the className into the selector string (with the class selector).
Or this will give you the same result.
$('#container ul li').filter('.' + className)...
Which is the similar to your .find() solution, but uses .filter() to limit the <li> elements found to those with the className.
If the element with the className is a descendant of the <li> element, then using .find() should work, or you could do:
$('#container ul li .' + className)...
...which almost looks the same as the one above, but introduces a space after li, which is a descendant selector.