let's / lets are similar-sounding terms with different meanings (referred to as homophones). To better understand the differences, see below for definitions, pronunciation guides, and example sentences using each term. 👇
let's: NA
lets: (noun) a serve that strikes the net before falling into the receiver's court; the ball must be served again. (verb) make it possible through a specific action or lack of action for something to happen. (verb) actively cause something to happen. (verb) leave unchanged.
let's: l·EH·t·s
lets: l·EH·t·s
(Examples are Wikipedia snippets under the CC ShareAlike 3.0 license. Definitions drawn from WordNet.)