You need to speak personally to an experienced immigration attorney, with the facts that you are giving in your question It is difficult to establish if you would qualify to adjust with the Diversity Visa, it is important to take into consideration that if at some point in time you accrued illegal presence that possibility could be ruined.
You can keep doing both processes, however if the DV lottery was legitimate, the finishing that process should be faster. Speak to an immigration attorney before making a decision.
If you already have an attorney, these questions would be better suited for him/her. Your attorney has all the details regarding your case, and is in a much better to address your concerns than the attorneys here on Avvo.
Jamahl C. Kersey (619) 399-3662 is an Immigration and Criminal Defense attorney licensed in CA. The answer above is provided for informational use only. One should not act or refrain to act solely based on the information provided. No attorney/client relationship is created unless an Agreement is signed by the attorney and the client. Best regards, Jamahl C. Kersey KERSEY & SABAWI 5703 Oberlin Drive Suite 201 San Diego, CA 92121 Tel: 619.399.3662 Fax: 888.765.5894 email@example.com www.kerseysabawi.com
You should speak to an experienced immigration lawyer to make sure you are admissible as a permanent resident. In some circumstances it will be better to adjust your status based on your asylum application because the waivers for inadmissibility are much more generous.