I know it wants とうとう for the answer here, but like… it’s lunch?? What is this, the restaurant at the end of the universe? 
Dramatic much?
In seriousness, asking those that have more first-hand experience speaking the language in an everyday-context… is this really a thing that’s likely to be said this way?
I think the problem with this sentence is that it’s missing a context to interpret one way or the other.
Might need a slight revision or add something before so you know you have to use とうとう instead of やっと.
I know what you mean. I had come across this before as well, but I just went with it. My main complaint is this hint appears to be making a distinction without a difference. In many instances, とうとう and やっと appear to be completely interchangeable, and the nuance of expectation vs. outcome is extremely blurry because the outcome and the expectation are one and the same. For example, consider these sentences from Tatoeba.
船はやっと母港についた。
The ship at length reached the home port.
私はやっと休むことができる。
I can take a rest at last.
父は五十歳のときやっと車の運転ができるようになった。
My father finally learned to drive when he was fifty.
All of these fit the nuance ascribed to とうとう in the grammar point description:
In what sense would saying “it’s finally lunchtime” not be an expectation but instead an outcome? If anything, I think やっと better fits this sentence. Lunchtime happens everyday. It’s not an outcome, but rather something we expect on a daily basis.
To @Megumin’s point, I think とうとう could be better indicated in the example sentence by perhaps indicating it’s a person who has been working hard in the ktichen who finally finished preparing everything, so now lunch can be eaten. But even in that case, I don’t see how やっと would be wrong. The person would probably be looking forward to lunch after having been spending all that time preparing it. There’s still an expectation element to the outcome.
goo.ne.jp defines these as follows:
The conclusion element is certainly there for とうとう, but the notion of spending time and effort to realize something is also present in やっと. If anything, for this sentence, it’s “after all” and “in the end” that don’t fit as well, which meanings are ascribed to とうとう, not やっと.
All that being said, the [final outcome] hint above the sentence is a strong indicator that とうとう is what’s expected. I just think the sentence could be better chosen or framed.
“Said by the head chef tasked with catering a luncheon for foreign dignitaries” 
