I grilled some fatty lamb chops hoping I could get the oil and use it as part of a sauce. However after cooking I relaised there was only a very little amount of oil in the lower pan.
Do you know what caused this e.g. too high temperature or maybe I didnt cook high enough, whats for sure though is the chops were cooked. Can you give me some guidance on how to extract all the oil from a protein to use as a sauce without making it disappear?
If you really want to render fat out of solid animal fat tissue, you need to cook it low and slow. There will be an initial period with a lot more bubbling and spattering as water is more rapidly released, then eventually it'll just be slowly cooking away, slowly releasing fat.
High heat methods like searing, broiling (UK grilling), and grilling (UK barbecuing) are pretty much the opposite of this. Everything just cooks fast, tightens up, and if you tried to cook long enough to release much fat, you'd probably just burn it all.
So I wouldn't think of fatty chops or steak as a good source of fat for this. You don't want to cook that meat low and slow, generally. So you'd probably have to trim the fat off to render slowly while you cook the meat on high heat, and there are way cheaper cuts of meat that you could get way more fat from, so why bother?
As mentioned elsewhere, fat is not evaporating. You might manage to burn a bit of it onto your pan, but given the above points, it's just that you probably just aren't getting a lot out of this.
A pan sauce is not so much about the melted fat, but, more importantly about the fond. In fact, too much oil is not helpful. The fond is the browned bits that stick to the pan. Water, wine, or stock is added to the pan. Using a wooden spoon, stir to release the fond and begin creating your sauce. Season with herbs. You can add some butter or cream...lots of variation from here...season with salt and pepper, etc. From your question, however, I see that you are grilling. I don't think a sauce is possible in that scenario. Maybe the better solution is a salsa for your chops.
