You state that you have a lawyer. That lawyer knows the facts of your case much better then I do from reading your brief post. I suggest you take the advice of your attorney or seek a second opinion from another lawyer. The lawyer from whom you seek a second opinion will need to review the circumstances of your case.
Stick with your lawyer. You can not file before October 1, 2012 ... which is the beginning of the US Government's 2013 'fiscal' year.
But, you may not be eligible to file on that date, depending on your number. Sometimes people with high numbers never get a visa.
Plus, having an asylum application pending may complicate your ability to adjust your status.
Trust your lawyer. If you don't trust him/her ... get a different one.
Capriotti International Law
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IMMIGRATION LAW PROFESSOR for 10 years -- LEGAL DISCLAIMER: This answer is offered for informational purposes only. It does not constitute an attorney-client relationship.
If you won, your effective date is oct 1. So nothing now. Then you must be sure that your number is available. On that date you need to be eligible for adjustment and your lawyer is telling you you are not. So the answer is probably no. But you need to move quickly on the case so either listen to your attorney or get a new one.