Look into Bonsai Ternary models. They're "1.5" bit models that have to be trained that way (so no taking a full model and quantizing it down) but they are so efficient and they can run on CPU only, though it's a bit alpha at the moment. Really cool company and projects.

You have to create a specific environment for them though, using Bonsai's GGUF version which enables them to run properly. So unfortunately, no use in LM Studio yet.