US out of status to apply work permit in los angeles

i am hoping somebody can give some light on this matter. I already have an approved LMO from HRSDC with the help of the company who is very willing to sponsor me. However, I would like to know if I can lodge my visa application in Los Angeles or not. My case for non immigrant visa application here in the US have been mishandled by my previous lawyer and because of that I am currently out of status. I have retained a new lawyer who is helping me with the nunc-pro-tunc case and the complaint we have filed against my previous lawyer. If I can show documents of this on-going case can the Los angeles embassy consider my application? If i file it in my home country it would take 5months to process while in Los Angeles it would only take a day or at least 2weeks. I am hoping someone has the same experience or at least some knowledge of this issue that could guide me in the process.

Thanks in advance..