In the future, please quote the entire sentence you're asking about because otherwise I have to listen to the exercise myself, trying to find it.

J'aime beaucoup le vieux Lille avec son architecture colorée.

There is no rule in French grammar that says that subject (Lille) and indirect object of a sentence (son architecture colorée) have to be of the same gender.

I assume you're aware that l'architecture is feminine (as indicated by the adjective colorée) and  the male form of the possessive pronoun (son) is used simply because architecture starts with a vowel.

Worked it out - architecture is feminine but starts with a vowel hence 'son'