It doesn't, that's a shame. It would definitely have to be a custom fork of either Clasp or Emscripten anyway because CL's "memory dump" way of creating executables would be too cumbersome to run in browsers. Someone might as well make a CL -> WASM compiler directly--in CL so that it could be more easily self-hosted.
I did a quick scan of the WASM standard, and there don't appear to be any instructions that let you e.g. add new functions, so it's not even clear to me how you would call WASM that you had newly generated.
