The words liar, lier, lyre sound the same but have different meanings and spellings. Why do liar, lier, lyre sound the same even though they are completely different words?
The answer is simple: liar, lier, lyre are homophones of the English language.
One that tells lies.
A person or thing that lies, in the sense of being horizontal.
Common misspelling of liar.
A stringed instrument of the harp family having two curved arms connected at the upper end by a crossbar, used to accompany a singer or reciter of poetry, especially in ancient Greece.
Definitions from The American Heritage® Dictionary of the English Language, 4th Edition, from Wiktionary, Creative Commons Attribution/Share-Alike License 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").