There is a lot of traffic on one side of the street.

A lot of traffic = many cars

There isn't any traffic in the street.

There aren't any cars.

A lot, some, and any are used with indefinite amounts:

Example:

Q: How many students are there in the classroom:

A: There are a lot. (This is a large number). Or....

A: There are some students. (This is a small number but the number is not known.) Or....

A: There aren't any students. (This is zero or a very, very small number and the number is not known.)