What is the added value for learning F# when you are already familiar with LISP?
F# is a very different language compared to most Lisp dialects. So F# gives you a very different angle of programming - an angle that you won't learn from Lisp. Most Lisp dialects are best used for incremental, interactive development of symbolic software. At the same time most Lisp dialects are not Functional Programming Languages, but more like multi-paradigm languages - with different dialects placing different weight on supporting FPL features (free of side effects, immutable data structures, algebraic data types, ...). Thus most Lisp dialects either lack static typing or don't put much emphasis on it.
So, if you know some Lisp dialect, then learning F# can make a lot of sense. Just don't think that much of your Lisp knowledge applies to F#, since F# is a very different language. As much as an imperative programming used to C or Java needs to unlearn some ideas when learning Lisp, one also needs to unlearn Lisp habits (no types, side effects, macros, ...) when using F#. F# is also driven by Microsoft and taking advantage of the .net framework.