Yes, it could be done in principle. The reason I chose C++ and not Fortran for the LFortran’s frontend is to have the whole compiler in the same language and to actually deliver a compiler. I can’t fight all the fights, so the first task is to deliver a working compiler that can also compile quickly (very important). If there is interest, we could write a new frontend in Fortran later once LFortran is in wide usage (currently it is not, so I am just focusing on delivering what we have).
What we have done already is to have the runtime library in Fortran, so if you want, you can already contribute to that here: https://github.com/lfortran/lfortran/tree/main/src/runtime, see the thread How to contribute to LFortran's runtime library for more info how to contribute.
GFortran and Flang could also in principle be implemented in Fortran, but chose C or C++ for the same reasons I think, to have the GCC and LLVM compiler collection in the same language, so that people need to only learn one language to contribute to it.