He can apply. It's far more complicated when it comes to processing. He cannot process in the USA. He would need to travel to his country and depending on his status and how long he has been out if status on the USA he may not make it back. Consult an Immigration Lawyer when it comes to processing .
He can apply.
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Whether he is in a valid status in the US does not matter. He can apply if he meets the other requirements related to education for example and is from one of the countries eligible to participate in the DV lottery. For example, China and india are not eligible to participate in the DV Lottery.
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