Her Majesty's Revenue and Customs lodged papers in the High Court on Monday to appeal the Company Voluntary Agreement with Portsmouth, which could prevent the club exiting administration.
The CVA, which was approved last month, would see Pompey repay unsecured creditors 20p in the pound but HMRC appealed against that decision.
Under Football League rules the club will stay in administration and under a transfer embargo until an appeal is heard, but a court has since ruled to speed up HMRC's appeal so an outcome should be reached sooner than originally expected.
Lampitt told BBC Radio Solent: "We've been in court in London this morning seeking an expedited process. That means we should have the hearing before the start of the season."
He added: "Therefore we should have some certainty on the outcomes prior to the start of the season. I'm yet to hear about the date for that hearing, but we should know within the next 24 hours."