"The young Arab boy is eating lunch where the Japanese cook is standing."
Translation:A fiatal arab fiú ott ebédel, ahol a japán szakács áll.
I can't think of any sentence where it would sound right to me but I don't rule it out completely.
In my opinion It's ok. "itt" or "ott" are not absolutely necessary to use in this sentence.
it's not just necessary but mandatory in this case, since the entire point of the sentece is to show that the two actions are happening in the exact same physical location.