I was told that ing can be used without an object e.g "the manager forbids smoking" while I know this is true, I want to ask if it can also be used with objects e.g., "I love making lasagne" or " the manager forbids smoking in his establishment." can the ing form be used like this also?
The Ving(Gerund) can be followed by an object or not, it is based on the context. For example, I stopped smoking. (In this sentence, the Gerund Ving is the direct object of the verb "stopped"). In your sentence: The manager forbids smoking in his establishment. (In this case, the Ving (smoking) is the direct object of the verb "forbids" and the phrase "in his establishment" is adverbial of this sentence, not the object, and this is correct in grammar.