The reason that Algernon gave to Cecily for lying about being Earnest is that A. He wanted to meet Cecily.
From the story, it should be noted that Jack is called Ernest in the city and Jack in the country because Jack has a younger brother named Earnest in the city.
The reason that Algernon give to Cecily for lying about being Earnest is that he wanted to meet Cecily. It wasn't because he wanted to get away from his aunt or to pay off Jack's debts.
