Lyla is Mr. Burns' cousin and former love interest.
Mr. Burns describes Lyla as the girl that got away. When Mr. Burns met Lyla, he fell in love with her. One day after drawing Lyla, he proposed to her. However, Lyla asked Mr. Burns to promise her one thing, which was to spend five minutes a day thinking of others.
Mr. Burns didn't agree to the promise and Lyla ran off in tears. In the present, she had gotten over her anger with Mr. Burns and had become a Buddhist. Mr. Burns was eventually reunited with her at The Peak Inn.
Just as Mr. Burns came out of the bathroom wearing white robes, Lyla was lying on the bed, deceased. Mr. Burns kisses her body and she disintegrates into dust.
Smithers advised Mr. Burns to do the one thing Lyla wanted him to do. Mr. Burns is seen working at a soup kitchen. Lyla is seen once more in the soup, telling Mr. Burns she's proud of him.