"A lot of" and "lots of" mean the same thing and are usually interchangeable.
"He makes lots of mistakes in writing" = "He makes a lot of mistakes in writing."
"He owns lots of cars." = "He owns a lot of cars."
However, there are a few fixed expressions where only one is used.
"That's a lot of nonsense!" = "Everything you said doesn't make sense."
but NOT "That's lots of nonsense". This one sounds strange.
When you're referring to something concrete and specific, we usually only use "a lot of".
Example: You're in a library and say: "Wow, that's a lot of books!" = "Wow, there are many books in this library."
"Wow, that's lots of books!" doesn't work in this situation.
Hope this helps. :)