"He has a difficulty with the lecture."
Translation:Tá deacracht aige leis an léacht.
na léachta is the tuiseal ginideach or genitive form - feminine nouns use na as the singular definite article in the genitive case.
But le doesn't cause the genitive. If you were using a "derived preposition" - réamhfhocail chomhshuite, you would use the tuiseal ginideach:
tar éis na léachta - "after the lecture"
i rith na léachta - "during the lecture"