Well this is precisely why we keep telling people to not lie with regards to immigration matters, it always comes back and bite.
Yes they already have your false information in the system, will it impact a DV selection or an immigrant visa petition? I don't know, the only way to know for sure is to give it a shot. If they didn't give you a document that says you've been found inadmissible, then there's hope.
Anyway, you need to bear in mind this is simply a lottery with about 1% chance of selection. So apply and get selected first, then worry about the impact of the previous NIV petition denial.
Thank you very much for replying.