where does the "a" come from in the English sentence? there is no "bir" in the Turkish sentence
I am sure lemon soup, with a little imagination, can exist. You just need the whole lemon. However, I would disagree with the above conjecture. ‘Limonlu’ could mean lemony. ‘Limon suyu’=Lemon juice. ‘Limon çorba’=Lemon soup, it is like describing the soup. But, ‘çorba limon’=The soup is lemon, also like describing the colour. But, ‘çorba limonu’ is the lemon soup itself (a soup made of lemons). To state ‘limon çorbasi’ is like stating that the contents of the lemon is the soup. It is like, ‘kırmızı palto’=the red coat, ‘palto kırmızı’=The coat is red, ‘palto kırmızısı’=a redcoat.
"limonlu" could mean lemony indeed. It just sounded weird in my head, so I dind't bother writing it, but you're right, that that would be the best translation.
Literally "limon suyu" means lemon juice, but in many cases you can just say lemon, since the whole lemon isn't used in most cases and this holds true in Turkish too, at least when discribing the contents of food, but you could say "limon suyulu (bir) çorba"
Regardless of previous statements "çorba limonu" is wrong. It would mean something like "soup lemon". Those are two nouns forming a compound noun so they don't follow the rules of adjectives, which you explained later, but follow the same rule of "domates çorbası".
They all follow the same rule and "lemon soup" would have to follow this rule too.