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As Caveman bases on Clack/Lack, you can choose which server to run on -- Hunchentoot, mod_lisp or FastCGI"
https://github.com/fukamachi/caveman/blob/master/README.mark...
Take a look at Clack. (Caveman2 is a web framework for Common Lisp, by Eitaro ("8arrow") Fukamachi; another recent web framework is Lucerne, by Fernando Borretti ("eudoxia0"))
Caveman is built on top of Clack and I think Lucerne is, too.
Another good option is Ningle, by Eitaro, which is a really mínimal minimal set of functions and macros to create a web application. Runs on top of Clack as well.