How can one atone for the sin of masturbating in childhood and lying to one's mother, knowing that one has repented and abandoned this sin permanently?

There is no sin upon you for what you did out of ignorance of the ruling, or before reaching puberty. Do not tell your mother anything about what happened, for it is prescribed for a Muslim to conceal himself with the concealment of Allah. Strive for righteousness, performing good deeds, abandoning evil deeds, and drawing closer to Allah.