Translation:I don't know what mom will cook tomorrow for lunch.
I think it is partially a situational difference. I made the same mistake while reading this too, but I believe in order to make the sentence into "i don't know , that mom will make lunch for tomorrow" it would probably have to be "i don't know , if mom will make lunch for tomorrow". "If" would fit the sentence better than "that". example “I wonder THAT this is wrong” & "I wonder IF this is wrong”. Don't worry many English speakers make this mistake, even me lol. good luck :)
I don't know if Duo accepts "I don't know what Mom is cooking tomorrow for lunch", but that form is what Duo discusses in the tips and notes: English using a present progressive tense to look into the future. A more accurate English statement is "what Mom will cook/will be cooking tomorrow", but "is cooking tomorrow" would definitely be heard often enough in American English to make it a correct usage.