In this new tutorial over on The Bakery, Anton Bobrov walks you through a process he discovered to get LightTPD and CakePHP setup in a subdirectory on his site.

I faced the challenge to install CakePHP under LightTPD. All works smoothly as long as I deploy projects in document root of domain. But when I want to setup CakePHP in subdir all goes wrong.

Basically, the tutorial involves changing some configuration options in the lighttpd to help it understand the correct routing for the CakePHP application. He even includes a download of the updates to make a drag & drop upgrade easier.