There's a funny quote from Kent Pitman
"...Please don't assume Lisp is only useful for Animation and Graphics, AI, Bioinformatics, B2B and E-Commerce, Data Mining, EDA/Semiconductor applications, Expert Systems, Finance, Intelligent Agents, Knowledge Management, Mechanical CAD, Modeling and Simulation, Natural Language, Optimization, Research, Risk Analysis, Scheduling, Telecom, and Web Authoring just because these are the only things they happened to list."
And, look, "web authoring" even made it on the list!
Lisp is good for web programming because it is so flexible and the s-expressions that make up Lisp forms have some nice similarities to HTML. To see what I mean, check out Lisp for the Web. Notice how he writes a macro to basically create a domain-specific language for creating web pages -- instead of defining functions, he's now defining pages! This DSL concept is also apparent in the CL-WHO library he's using, which lets you write Lisp that turns into HTML.
Paul Graham had success rolling his own solution while creating what later became Yahoo! Store in Common Lisp (and even more success writing about it afterwards), and since then many packages have sprung up.
Weblocks is the Common Lisp web framework that seems to me to have the most momentum at the moment. There's a video of it being discussed at the Twin Cities Lisp user group. UCW is very similar, but I don't see much action on it now (please excuse me if I'm just looking in the wrong places). The blog post on why the creator made Weblocks is pretty enlightening: he basically wrote enough Lisp so that he'd never have to deal with HTML, AJAX, and JavaScript again. That might be an overstatement, but the fact that he could even do some of that should answer your question.