which form of verb we should use with a lots of and a number of?

The form of the verb will depend on the noun used with ' a lot of'. It will depend on whether the noun is singular or plural.

For example: A lot of sand was there on the beach.

A lot of the apples were rotten.

In simple words, 'a numbe'r of' is a substitute for 'they'.

It will get a plural verb.

For example: A number of the boys have eaten.