Bluntly put - I am not at all sure you can 'install' PHP-APC in LAMPP (at least without a lot of work). I'll do some checking, but I suspect you might need the LAMPP developer package. I'll let you know what I find out.
Did you know that LAMPP has a PHP accelerator included? Its 'e-accelerator' and its part of the basic LAMPP package. I have not tested e-accelerator on the XAMPP for Linux package (as I am in the midst of a large PHP development project on my LAMPP box), but I have tested it on the XAMPP Windows version and it worked quite well.