Many years ago, at the tender age of 14, I had an English teacher who made it his mission in life for his students to learn that a lot was actually two words not one. I can't say what led to his over exuberance of this particular subject, but I can say that it did make an impact on me. However, I realize that people still have trouble with these two little words. I see it misused all the time on twitter, facebook, emails, etc. So if this is a problem for you, don't lose heart. You're not alone.
Let's start off with the definition of lot, according to Merriam-Webster:
a considerable quantity or extent
Ex: I have a lot of homework.
The a in front of lot is an article that works as an adjective. It in no way is part of the word. Just think, you wouldn't say alittle or abunch. You would automatically know that wasn't right. But just as little and bunch are words that measure the quantity of something, so does lot.
If you still have trouble remember, Hyperbole and a Half has a great illustration that is hilarious and informative.