I've deployed a couple sites for customers on Hunchentoot, one using CLSQL with PostgreSQL. Unfortunately, that one's covered by an NDA. The other, I can talk about, but I won't post the URL as the nature of the application means that random people using it would only serve to irritate the customer.
It's a web-based file transfer system allowing anyone to send files to the customer's employees and the employees to send files to anybody. It sits behind Apache using mod_proxy and gets its main template by loading a Wordpress page over http. Wordpress can play nicely with it since the html template library does everything in comments.
Hunchentoot is really nice and hackable. One highlight: I added an :around method on dispatch-request to check to see if an IP is banned, and handle the request appropriately.
Like most Lisp web systems, you can get a REPL on a running server. I use detachtty for this.
You have a few options for how to install the app (lisp source, fasls, core images and with some lisps, a self-contained executable). They all work.
It's not a framework. You can do things how you want to without having to fight with your libraries.
I had some problems deploying on a VPS (Mediatemple DV plan, to be specific). SBCL and CMUCL didn't want to run, complaining about a memory allocation error. Limiting memory usage with the --dynamic-space-size argument works, but means setting a static memory limit for your app. I haven't had problems on two other VPS hosts, but some other people have.
You'll want to
(setq cl-ppcre:*use-bmh-matchers* nil)
or you may run out of memory anyway. In fact, you'll probably want to do that most times you use cl-ppcre.
It's not a framework. You'll have to decide how to do everything, often choosing between several libraries with no obvious best choice, or writing it yourself.