So I opted for fast instead of proper cooking, and for once lucked out.
I'd had a vague idea of trying something like the sauce I had on fish at a Greek restaurant in NYC on the lamb, but we didn't have all the ingredients...and I wanted potatoes, but time had run out. What we had was a can of chipotle diced tomatoes, a can of sliced new potatoes, and the last tablespoon or two of capers in an almost-empty bottle. I took the lamb out at the medium-rare stage, and while it rested on top of the stove I combined the above ingredients in a saucepan and heated them up.
Lamb slices with potatoes, the chipotle diced tomatoes (which, according to the can, also had onions and garlic in the mix) , and capers was...incredible. Lamb was tender and pink, the sauce complemented it amazingly well and the potatoes had taken up some of that flavor.
This will happen again.