Are you able to use eggs? I make these oat flour biscuits fairly often and they are quite good. I use oat milk but any non-dairy milk substitute should be fine.
I expect subbing the butter for lard or non-dairy butter substitute (I have heard good things about Earth Balance) would not be a problem. They can be a bit crumbly, but if that’s a problem you could probably add some xanthan gum or an extra egg.