This sentence means two things, from what I can tell. "Do they eat lunch?" and "Are they having lunch?" There is no context to tell you which meaning this is, and both meanings are accepted by Duolingo. But if I encountered this sentence "in the wild", I would not really know what the speaker was asking.
Could I say this sentence as "Do they have lunch?" or "Do they lunch?" (verb to lunch as in potuguese almoçar) meaning to ask, for example, if a particular people or a comunity has the concept of "lunch" and if they instead just eat a lot of small snacks during the day? It's silly I know but I'm just curious because this is the way I would try to express this kind of idea... As to the "Are they eating lunch?" I would think of something as "Ĉu ili estas tagmanĝas"
You can't use two conjugated verbs one after the othr, like you did with "Ĉu ili estas tagmanĝas?" because the second verb would need to be the infinitive form - in this case, tagmanĝi. That aside, the sentence does not work, because people cannot be a verb. If you feel the need to be completely unambiguous without context, you could use participles to clarify your sentence. "Ĉu ili estas tagmanĝanta?". This is the same way that English treats "eating" in "Are they eating lunch?" - eating is a present participle.
Please tell me why there is no 'a'? It is question about one lunch, is it not?