I cook with ghee (clarified butter) more than the pasture butter in my fridge. Ghee tolerates a much higher temperature because the milk solids (which burn) have been removed. You can make it yourself. If you are using olive oil for high heat (not a terrible thing) cooking, add a bit of ghee to it and that will help minimize burning of the oil.
coconut flour will be less sensitive to the heat of baking (little PUFAs!), but my guess is there will be oxidation. It is so much more stable than almond flour, for instance. It is high fiber, so you will need to use more liquid (for each portion of flour I add an equal amount of liquid/egg). Bake at a lower heat...
LARD is a great but not that easy to find, I think. I save my bacon grease for cooking. It also tastes SO good in a salad dressing.
That is what I think I know. I am sure others will correct me! I don't fry foods, so I have no answer for what oil to use for deep frying if that is something you are interested in.