If you're going to cook all three at the same time, something is going to be hotter than it should be or colder than it should be. If you're not making a soufflé, or something very small like cookies, you have a little flexibility and variation in temperatures.
- if something is in a hotter oven than called for, it will cook more quickly and perhaps brown more than you wanted as well,
- if something is in a cooler oven than called for, it will cook more slowly and perhaps brown less than you wanted as well.
You can adjust for the speed issues by having it in the oven for a longer or shorter time than called for. You can fix the browning by covering it with foil, or giving it some time under the broiler at the end - the latter being more reliable than the former.
I don't know about your potatoes but I'll assume they need to brown. Here is how I would run it, for a 6pm dinner:
- 4:00 preheat the oven to 450
- 4:10 put the lamb in
- 4:30 turn the oven down to 400
- 5:00 put the potatoes in. They're going to get 15 minutes extra time to make up for the cooler temps
- 5:30 take the lamb out for a 30 minute rest (sure, your recipe probably says 15, but the extra time won't hurt.) Turn the oven down to 350 and put the beans in.
- this final half hour is when you make the gravy and whatever other side dishes are involved, set the table, etc
- 5:55 check the beans. You can probably take them out and let them sit for 5 minutes. Check the potatoes. If you want them browned, now's a good time to put the broiler on above them.
- 6 pm serve
By the way, I wrote this timeline from the bottom up and you can do the same next time you're trying to work out timings.