While this is the case for almost all animals and their meat in Japanese, oddly enough lamb meat is ラム肉 ramu-niku, where ramu is loaned from English "lamb". The animal is 羊 hitsuji, but while 羊肉 youniku is possible, you'd rarely if ever use that in speech (and I had to look up the onyomi reading!).

That said, lamb is quite rare in Japan, it's eaten primarily up north in Hokkaido.