Hi there
This is my first time here. I made asylum application on 25/01/2005 and it was refused in March then appealed but refused and gave me 5 days to appeal unfortunately my lawyer didn't log my appeal then the next hear from UKBA said my application was exhausted and have outstanding application. I wrote to Legacy case solution in Croydon but no answer been received. I also wrote to Liverpool but nothing from them. My questions are'(1) What can I do? (2) Any best lawyer who solve my situation?

Sounds like you are out of luck due to the number of appeals being exhausted.
Time to arrange for a return to your country of origin.