If your girlfriend is a green card holder and acquired her green card through the DV lottery, then you will not have a visa number immediately available upon marrying her. A green card holder's spouse petition takes about 2.5 years to become current. This means that you will not be able to stay in the US to adjust your status. Depending on how long your girlfriend has had her green card, it may be wise for her to become a US citizen first, then file an immigrant petition for you. Good luck.
This information is intended as general information only. This communication does not establish an attorney-client relationship between me and the asker.