First install Emscripten via your distribution's package manager or download and install it yourself. Then build asm.js and WebAssembly binaries using
mkdir -p build/emscripten cd build/emscripten emconfigure cmake ../../src -DCMAKE_BUILD_TYPE=Emscripten make lean_js_js lean_js_wasm
This will produce files lean_js_js.js, lean_js_wasm.js, and lean_js_wasm.wasm in shell/, which you can e.g. copy to the dist/ directory in lean-web-editor instead of calling ./fetch_lean_js.sh there.