I am assuming that you are a veterian. If you applied for DV2004 you must not be ineligible.
As a J-1 visa holder, you may have the burden of returning home for a two year period following your training. You need to see if section 212(e) does or does not apply. If training was paid for by the government, chances are it will apply. As an h-1 you do not have that problem.
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