The words lain, lane sound the same but have different meanings and spellings. Why do lain, lane sound the same even though they are completely different words?
The answer is simple: lain, lane are homophones of the English language.
Past participle of lie1.
A narrow country road.
A narrow way or passage between walls, hedges, or fences.
A narrow passage, course, or track, especially:
A prescribed course for ships or aircraft.
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").