It’s not so much that I see this pair of words used instead of each other, but unfortunately a number of people get the first one wrong.

a lot: a large extent, often, many. Note it is two words.
She has been using the writer a lot for this project.

allot: to distribute or assign parts of something
The manager will allot tasks to his team.

The word alot does not actually exist – it is simply how ‘a lot’ sounds.