I find rack of lamb to be one of the easiest meats to nail for doneness. You've summarized it well. It seems to have an aura about it that people find it to be intimidating.
I love Ina's rub and prep for lamb. In fact I served that for some of our fellow posters a few years ago.
Just looked it up. Looks like Ina's rub would be freakin' delicious. I'll have to give that a shot.
As for nailing for doneness, I think it's very easy if you use a thermometer. If you're trying to cook to time rather than temp, or if you're trying to cook to "feel", it's much harder. Lamb is a much smaller cut of meat than, say, prime rib, so the time window between undercooking and overcooking is very narrow. Ina's recipe says exactly 20 minutes at 450 degrees, but that's assuming your oven is accurate. It also that your racks are the same size as what Ina tested on, which is difficult because Ina doesn't say what size she recommends, and there can be a lot of variation, particularly between Australian/New Zealand lamb (grass fed and smaller) vs American lamb (often grain-finished and larger). And of course it assumes that they were trimmed the same way, etc. I.e. if you trim lamb to "lollipop" size the way I do, it will naturally cook faster than if it's trimmed
the way Ina shows it in her Food Network recipe, where the fat cap is left on.
And this is especially important when you grill rather than roasting in an oven, because it's a lot harder to pick a "precise" temp on the grill, especially if you do it the way I do it first and sear it directly over high heat. I can't translate Ina's recipe of 450 for exactly 20 minutes to a grill where I sear it over ~600 degrees for 5-6 minutes total and then put it indirect at an unknown temp. Granted, Ina's recipe is for oven-roasted lamb, so that's fine, but if you like the taste of searing over direct heat, then you need to know up front the temperature you're trying to hit.
I wish more recipes online would not only convert to measure ingredients by weight instead of volume [where appropriate], and would convert to giving you the exact internal temperature to cook to for appropriate doneness than by time. Recipes assume that home cooks don't have a precise scale or a proper leave-in oven thermometer or even an instant-read thermometer, so they want to make it "easy" instead.
But yes, with a thermometer you can hit perfect doneness on lamb very easily.
If I'm spending $14/lb on racks of Australian lamb, cutting away and discarding big portions of the fat cap and obviously some of that weight being paid for is bone, I'm going to use the technology necessary to make sure I don't f&#@ it up and undercook/overcook it. Especially since we were having company over and I'm potentially being judged if I do it wrong.