The difference between a lot and alot
The difference is fairly definite. A lot is correct, alot is not.
a lot (adverb)—a great amount, much
There was a lot of cleaning up to do after dinner.
While I have some very early school work which clearly shows me writing alot, they were also accompanied by my teacher’s trusty red pen, notifying me of my mistake. Hey, I was only six!
It might be the case that the mistaken use of alot is down to the word allot looking so similar. However, since allot means to distribute or give out portions of something, there’s no reasonable explanation for the presence of alot at all. It’s just down to laziness or naïvety on the writer’s part.