Peter gave a great answer... I'll expand on it a little.
Lift gives you a ton of control and access to raw HTTP requests as well as providing a ton of abstractions on top of the HTTP level. It's your choice on how much or how little you want Lift to do.
You can built a REST-based application using Lift's RestHelper. See http://simply.liftweb.net/index-Chapter-5.html The advantage that Lift's RestHelper gives you over most MVC/Routing based approaches is type-safety and access control at the very edge of your application. But using Scala's pattern matching extractors, you can insure that parameters delivered to the business logic of your application have already been materialized and checked for access control. Further, Lift's REST support will be as concise or more concise than other web frameworks.
In terms of Lift's HTML handling, you have a ton of control over the creation of the HTML, as long as you want to generate HTML as a valid DOM rather than as a series of Strings.
Most web frameworks force you to emit Strings when you're composing HTML. It's up to the developer to properly HTML-escape Strings. It's up to the developer to make sure that closing tags line up correctly. With Lift, you get this kind of thing for free.
You can serve HTML from Lift apps in MVC style. See https://github.com/dpp/hoisted (this is the code that powers http://liftweb.net)
In the "standard" configuration of Lift apps, Lift does some post-processing of the HTML if, and only if, you use certain construct. So, if you put a <head> tag in the body, the HTML page, Lift will take the contents of that <head> tag and move it to the head section of the page. If you include calls to Lift's Comet support, Lift will insert JavaScript on the page to do long polling. But these features are optional and they only happen if you use certain features in Lift.
I hope this helps you understand the benefits of using Lift.
