In this sentence, where is the object?
Anna ate her cold chicken sandwich for lunch.
her cold chicken sandwich
The question that you can ask to check this is "What did Anna eat?" or "What did Anna eat for lunch?"
Paring it down to the minimum, it's "sandwich", because "her", "cold", and "chicken" are all being used as adjectives. And "for lunch" is a prepositional phrase also being used as an adjective modifying "sandwich". In this phrase, "lunch" is the object of the preposition; it is not the object of the sentence.