One of SBCL's claims to fame is that it doesn't necessarily require a previous copy of itself to bootstrap; it can in theory use CLISP or Clozure CL. (In practice it isn't always tested and working, and I don't know if it would work on ARM if you tried it today.)
The catch, of course, is that building from source requires a pre-existing SBCL to bootstrap.
My guess is the only way to get it running on ARM right now is to get it for a non-ARM platform they have for download, bootstrap to 1.2.0, and then cross compile to ARM.