Sheep can be slaughtered for meat at any age. The younger the animal is, the more tender, mild, and paler the meat is. But of course that means there a whole lot less of it. The older the animal, the more meat.
...Newborn lamb. 1-3 days old. Normally this is only done when the pelt is wanted, or you have a bummer you don't want to hand raise. But the meat is quite edible, being soft, pale, and "sweet". There's just not much if it. I find its best used for soup.
...Baby lamb (also called young lamb) is a traditional Easter meal. 6-8 weeks is the usual age.
...Spring lamb is 3-5 months.
...Lamb is up to 1 year of age.
...1-2 years old is a hogget, though I've heard via the grapevine that the rules have changed to allow a hogget to be labeled lamb. Perhaps that's why store bought lamb tastes so strong nowadays.
...Anything over 2 years old is strictly mutton. Personally, I think anything over 1 year is mutton.
Mutton is darker colored, tougher, and stronger flavored. Both hoggart and mutton improve with hanging or aging for 7 days, but no sheep meat actually needs to be hung or aged to be decent. Since I don't have a facility to hang a sheep carcass, I simply age the meat in the bottom of my chest refrigerator where the temperature is about 35°. Personally, I prefer to grind up mutton rather than butcher it into cuts.
By the way, I don't hang or age my lamb. And I prefer 3-4 month old spring lamb to anything else.