Dear @Lizy,
Welcome to the Wefugees Community and thank you for reaching out to us.
Unfortunately I am absolutely not familiar with the US DV lottery and can only make some research. I am sure you studied this website already? If not, you may check it for the general requirements, including a list of "excluded countries".
I can only say that your asylum procedure in Germany would most probably be closed as soon as you leave the country.
Maybe other community members can share more information or experience in this matter.
In any case, please also don't hesitate to get back to us with any further questions.
All the best,
Meike