The words lie, lye sound the same but have different meanings and spellings. Why do lie, lye sound the same even though they are completely different words?
The answer is simple: lie, lye are homophones of the English language.
To be or place oneself at rest in a flat, horizontal, or recumbent position; recline: He lay under a tree to sleep.
To be placed on or supported by a surface that is usually horizontal: Dirty dishes lay on the table. See Usage Note at lay1.
To be or remain in a specified condition: The dust has lain undisturbed for years. He lay sick in bed.
To exist; reside: Our sympathies lie with the plaintiff.
The liquid obtained by leaching wood ashes.
See potassium hydroxide.
See sodium hydroxide.
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.
If they are spelled the same then they are also homographs (and homonyms); if they are spelled differently then they are also heterographs (literally "different writing").