There are a lot of people,
we use the form of be Are because you have to use the correct form of the verb according to the subject and in this case people is the plural form
person ( singular)------- people ( plural)
a lot of is a quantifier, which means it's a word that helps count in a general way, you can use it for countable and uncountable ( non countable) nouns.
There is a lot of traffic today ----- traffic ( uncountable)
there are a lot of stores----- stores ( countable)