You tell a friend, â“you must be busy. i'd better let you go,â” because you want out of the conversation. what type of lie did you use?

The type of lie that you use in this situation is: Hinting

Hinting is a type of lie by not directly said a lie but by passively influencing someone to choose a decision by revealing specific information.
Another example of hinting: saying "You must be a lot fitter than me. I guess i wouldn't be able to keep up with you on the hiking trip" as a way to avoid going hiking with your friends.