The reason for not supporting eval is that this is a source-to-source compiler like CoffeeScript, not a run-time environment.
I wasn't paying attention and thought you meant LavaScript was written in CoffeeScript...
but I'm starting to doubt that this language can (or should) support full-fledged quasiquotation
I think I'm starting to get it: it's not that you couldn't support full-fledged quasiquotation if you wanted to by writing out an implementation in Javascript, it's that it wouldn't be very useful without being able to write macros via functions written in LavaScript, which in turn would mean that you'd have to be able to support loading LavaScript programs incrementally, which would mean having the LavaScript compiler in the runtime environment.