Mainline Lisp, which is for the most part stuck in amber with Common Lisp.
Scheme, which is semi-stuck in its MIT design style "do it right or not at all".
Clojure, the new hot Lisp that many think is the future of Lisp.
Scheme made some major departures from mainline Lisp, only one of which was adopted by the later (static scoping and all that implies (I now forget how good its support for closures is)).
Clojure is a further departure: not very multi-paradigm (and much more functional than Scheme) and its unification of data types (lists, maps, etc.). It's also like Scheme in getting rid of a lot of legacy cruft (starting with cons!) but is not an essence of purity language like Scheme, e.g. while a Lisp-1 it has mainline Lisp style macros.
So I'd say it's "more modern", e.g. its embrace of STM, which is an idea of the mid-80s to mid-90s. Most other new Lisp dialects strike me a "yet another Lisp"; I'm not sure about Arc, though.
I agree at least in part with the comment you are replying to, a modern language needs concepts newer than the '60 and 70s (closures are I think the only '70s concept in what Flow enumerated).
While its mathematical roots are fairly old, aggressive Hindley–Milner style type inference is I think a "modern" language concept. '70s at least???