<p>At the moment I use PHP for almost everything I develop for the Web but its linguistic limitations are starting to annoy me. However, as I developed some practices and maintain some PHP libraries that help me a lot, I don't feel I'd be ready to just switch to LISP throwing away all my PHP output. It could even be impossible on the servers where all I have access to is a regular LAMP hosting account.</p>

<p>Ergo, my questions are:
Could LISP code be just combined with PHP one? Are there solutions for side-by-side LISP/PHP, interface for their interoperability or perphaps just an implementation of one for the other? Or is it a mutually exclusive choice?</p>

It's not a mutually-exclusive choice, you can run both on one system, in the same way that perl and php (for example) are run side-by-side on many systems.
There's a
good post here
on a similar topic, which suggests using sockets to communicate between both languages -
If you want to go the PHP<->Lisp route the easyest thing to do would be to make PHP communicate with your Lisp-process using sockets.
http://php.net/manual/en/ref.sockets.php
http://www.sbcl.org/manual/Networking.html
This approach does still leave you with the potential added complexity and maintenance issues you get from having 2 languages in your project, but might be a fit for your particular use case.