If you ask for my opinion, I think that the word[s] "a lot" should be spelled without a space between the "a" and the "l".
Why the space? It doesn't do anything for the word[s], it doesn't make it look better, all it does is take up extra space. No pun intended.
So, I think that since the space is superfluous, everyone should just write it without a space. I don't know if anyone else does this, but I always write it without the space, then as my laptops underlines it in red, hitting the delete key four times, then rewriting it the "right" way.
The space seems unnecessary. At least to me.