Is there a rule of thumb for the weight or cut?
I'd prefer to err on the side of well-done, as I want to serve it to my toddler.
Treat it like beef steak. Super-hot pan, slap it on, keep pressing it with your finger, when it feels very firm, it's well done; about 5-6 minutes a side in general but it will depend on thickness; the finger test never lies. Let it rest for a few minutes after cooking.
If you're going to go for well done, you might want to consider a braise. Sear the steaks on both sides, the add some liquid (red wine, chicken stock) and veggies (onion, celery, carrots, mushrooms, garlic), lower the heat and cover. Cook until it is falling apart tender. It's not necessarily the best way to do a steak, but since you are already going to well done, which tends to make a steak tough, this will give you well done, but tender.
The above is not exactly a recipe, but a technique, you can find any number of braises that will work for you.
It really depends on the thickness, temperature of cooking and whether the meat has warmed to room temperature first. Can you give any more details?
I agree for lamb leg you might want to braise for tenderness; however flavor is a different matter. A technique which has the bonus of tenderizing while letting you do a lot of the prep ahead of time may be useful. Seal the meat portions, together with any herbs or marinade, in a ziploc bag with as much air squeezed out as possible. Fill a cooler/icechest with hot tap water, plus a small pot of boiling water. You will get something around 140-160 degrees F (obviously the more boiling water the hotter it will be). Immerse the ziplocs and close up the cooler for 12-24 hours. Depending on how cold your meat is and size/type of the cooler, you will only lose a degree or two per hour. Afterward take it out of the bags, throw it in a very hot pan for a few minutes on each side. The short cooking will mean you dont dry out the meat; the long bath means it can be tenderized.
But don't assume it has to be well done! Tastes vary - my five yr old daughter has always loved rare and still tries to sneak bits of raw meat; my older son likes it so well done it's practically dried out.