The words laps, lapse sound the same but have different meanings and spellings. Why do laps, lapse sound the same even though they are completely different words?
The answer is simple: laps, lapse are homophones of the English language.
The front area from the waist to the knees of a seated person.
The portion of a garment that covers the lap.
A hanging or flaplike part, especially of a garment.
An area of responsibility, interest, or control: an opportunity that dropped in his lap.
A moral fall: a lapse from grace.
A break in continuity; a pause: a lapse in the conversation.
To fall from a previous level or standard, as of accomplishment, quality, or conduct: lapse into bad habits; a team that lapsed into mediocrity halfway through the season.
To deviate from a prescribed or accepted way: lapse into heresy.
Definitions from The American Heritage® Dictionary of the English Language, 4th Edition and Wordnik.
Homophones (literally "same sound") are usually defined as words that share the same pronunciation, regardless of how they are spelled.