What is the difference between 'a lot more' and a lot or more?
A lot of fun
A lot more fun
Going to the cinema was fun.
Going to Disneyland was more fun than going to the cinema.
Going to Disneyworld in Florida was a lot more fun than either the cinema or Disneyland!
Remember that "more fun" and "a lot more fun" are both comparatives, so there would have to be something else mentioned that you're comparing something with.
Let's go to the park. It will be fun.
No, let's go to the beach. That will be more fun!