Does your body metabolise lipids?

I was under the impression that this was the case when all glycogen stores and immediate glucose in the blood ran out and that it was only used in cases of extreme need and in times when lots of oxygen is available due to the vastness of the molecule and the amount of H+ ions it coincidently provides (hence the oxygen demand required for electron transfer chain) for chemiosmosis in the ATPase enzymes of the inner membrane of the mitochondria. Recently though a teacher/lecturer at my college announced that lipids were not respired (my confidence with her isn't the greatest from previous other comments) and I thought this a strange thing to believe. I mean if we didn't metabolise lipids then the only way of using up your stores is in the general use throughout the body e.g. cell membranes, LDL/HDL etc and that would mean losing body fat would take a very long time and we all know it isn't that slow. Anyone who has ever been ill for a few days and not being capable of eating, will know your body fat plummets like a stone. So really my answer is does your body use lipids as a source of ATP synthesis and if so what is the metabolic pathway name so that I can look up the unique sequence of reactions for lipids in general. I have studied respiration in terms of glycolysis, the link reaction, krebs cycle and the electron transfer chains involved with ATPase for carbohydrates and amino acids but we glanced over lipids and fats and I was wondering about lipids in particular. Thanks.