The words lesson, lessen sound the same but have different meanings and spellings. Why do lesson, lessen sound the same even though they are completely different words?
The answer is simple: lesson, lessen are homophones of the English language.
To make less; reduce.
Archaic To make little of; belittle.
To become less; decrease. See Synonyms at decrease.
Something to be learned: lessons from observing nature.
A period of instruction; a class.
An assignment or exercise in which something is to be learned.
The act or an instance of instructing; teaching.
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.