Kuzu - lamb/the lamb/a lamb
Bir kuzu - a lamb/one lamb
Kuzuyu - the lamb (only when it is recieving the action)
Köpek - dog/the dog/a dog
Bir köpek - a dog/one dog
Köpeği - the dog (only when it is recieving the action)
Hope that helped!
Sources: Duolingo and my Turkish friend :D
You need some article per se (unless "küçük kuzu" is used as a name, for example, a character "Little Lamb" in a play). As far as I understand from other discussions, the indefinite article is mandatory whenever the noun is accompanied by an adjective (and then preceeds the noun - küçük bir kuzu). When there is no indefinite article, the definite article is implied, which makes it "THE little lamb" and "THE big dog". Was that your question?