Isn't the 'che' superfluous? "Cos'è lui?" would already mean 'What is he?'
"Che cosa" = "Cosa", both versions should be accepted.
When I was at elementary school my teacher wanted me to write every time "Che cosa", but I think that was a bit too strict. Italian is a very flexible language, if the version "Cos'è lui?" is not accepted, you should try to report it. :)
I was taught that "Cos'è" is a contraction of "Cosa" and "è", because it would otherwise sound weird transitioning between the two vowels. If you're talking at a normal conversation speed, it'd blend together anyways. It's less lazy that English contraction that seem to be caused by "I don't feel like pronouncing this vowel".
This might be helpful if you're also familiar with Spanish or French: I think of the Italian "che" the way I think of the Spanish "que" blended with properties of the French "qui" and can mean "what/that/which/who" depending on the context.
Anyone else have input on this? (Because I just made it up...)