lot

Concise Oxford English Dictionary © 2008 Oxford University Press:
lot/lɒt/

▶pronoun (a lot or lots) informal a large number or amount; a great deal.

■ (the lot or the whole lot) the whole number or quantity.

▶adverb (a lot or lots) informal a great deal. ▶noun

• 1 [treated as sing. or pl.] informal a particular group or set of people or things.

• 2 an item or set of items for sale at an auction.

• 3 a method of deciding something by random selection, especially of one from a number of pieces of paper.

  ■ the choice resulting from such a process.

• 4 a person's destiny, luck, or condition in life.

• 5 chiefly N. Amer. a plot of land.

  ■ (also parking lot) a car park.

▶verb (lots, lotting, lotted) divide into lots for sale at an auction.

– phrases
bad lot Brit. informal a dishonest person.
draw (or cast) lots decide by lot.
fall to someone's lot become someone's task or responsibility.
throw in one's lot with decide to share the fate of.

– origin OE hlot (n.) (orig. in sense 3 of the noun, sense 4 of the noun), of Gmc origin.

usage:
Although a lot of and lots of are very common in speech and writing, they still have an informal feel and it is better to avoid them in formal English, where alternatives such as many or a large number should be used instead.
The correct spelling is a lot; the one-word form alot is incorrect.