The words leave, lieve sound the same but have different meanings and spellings. Why do leave, lieve sound the same even though they are completely different words?
The answer is simple: leave, lieve are homophones of the English language.
To go out of or away from: not allowed to leave the room.
To go without taking or removing: left my book on the bus.
To omit or exclude: left out the funniest part of the story.
To have as a result, consequence, or remainder: The car left a trail of exhaust fumes. Two from eight leaves six.
Same as lief.
Definitions from The American Heritage® Dictionary of the English Language, 4th Edition, from the GNU version of the Collaborative International Dictionary of English and Wordnik.
Homophones (literally "same sound") are usually defined as words that share the same pronunciation, regardless of how they are spelled.