Both lots and a lot of are nouns for amounts of things or quantifiers. They are used when the amount of something is known to be large, but an exact counting isn’t necessary. Both are used in more informal speech and writing. More formal word choice would include many or much.
Side note: A lot of is sometimes spelled alot, which is incorrect.
Some say that lots is the plural form of a lot of. While that may have been the case in the beginning, now they are more like synonyms, with lots being even slightly more informal than a lot of. Both can be used with singular or plural objects.
Gardaí have made one of the biggest heroin seizures in Cork this year, which they say “would have done a lot of damage”. [Irish Examiner]
Dr. Omar has a lot of publications on his name on a range of topics including democracy, current political affairs, and strategic relations. [Somaliland Sun]
“Candy bars don’t even have a lot of chocolate in them,” Schroeter said. [Boston Globe]
Suddenly National Chocolate Day seems less like an excuse to eat lots of chocolate, and more like a reason to celebrate one of Earth’s greatest foods. [Inquisitr]
That means lots of students like Johnson have to make calculations: Draw school out so there’s time to save up — putting yourself at risk for dropping out altogether? Or take on more student loan debt? [NPR]
For some, the holiday season is about spending lots of money on expensive gifts. [Lexington Herald-Leader]