A Lot of, Lots of and a Lot are used in informal English. A Lot of, Lots of and a Lot mean ‘a great quantity of’. Beside that, A Lot of, Lots of and a Lot also have meaning ‘large number of’. I will describe it one each one.
A lot of / lots of
A lot of / lots of can be used before a countable or an uncountable noun. Example:
• A lot of people want to buy cars.
• A lot of money was wasted on the project.
• I have a lot of work to do.
• There is a lot of meat left.

Verbs are a lot of / lots of
There is a condition when the verb is plural. This will happened if a lot of / lots of is used before a plural subject. But, the verb becomes singular if these expressions are used before a singular noun. Example:
• A lot of patience is needed to learn a new language. (NOT A lot of patience are needed to learn a new language.)
• A lot of my friends live abroad. (NOT A lot of my friends lives abroad.)
A Lot
A lot means ‘a great deal’. It can be categorized into an adverb. You should note that a lot is not followed by a noun. I will give you example:
• I like him a lot. (NOT I like him a lot of.)
• She reads a lot.
• James travels a lot.
Notes
The expressions a lot of and lots of are rather informal. We prefer expressions like ‘a great deal of’, ‘a large number of’, much or many in formal use. Here is an example:
• A great deal of time is needed to learn a new language.
A lot of and lots of are not normally used in questions or negative sentences.