Let’s is a contraction of let us, often used as an imperative. If one can replace let’s with let us, then it is a contraction and therefore, needs an apostrophe. The use of contractions is not a modern phenomenon, contractions came into use during the period when Old English was spoken, though the use of an apostrophe to mark the place of the missing letters didn’t come into usage until much later.
Lets is the past and past participle of the verb let, meaning to allow, permit to escape or flow, to allow to go past or come forward. In British English, let means to rent to a tenant, it may also be used as a noun to refer to the space which is being rented. The verb let comes from the Old English laetan, meaning to allow to remain, let go, leave, depart from, leave undone, to allow, bequeath.
Cloud A Commodity? Let’s Not Draw Wrong Conclusions Again (Forbes)
Robert Hively-Johnson: Let’s act as if all lives matter (The Winona Daily News)
In this process let’s also demonstrate we can support McMillian’s development without losing the essence of our highly regarded McMillian Mesa/Buffalo Park treasure. (The Arizona Daily Sun)
The Virginia Shooter Wanted Fame. Let’s Not Give It to Him. (The New York Times)
Goa police launch app that lets citizens file complaint online (The Times of India)
New York City Website Lets Users Drill Deep Into Census Data (The Wall Street Journal)
Strange physics trick lets people create a cloud in their own mouth (The Irish Independent)
In landmark case, labor board lets more workers bargain with their employer’s employer (The Washington Post)