I get "I bought a lot of clothes", but not "I like that a lot". Before the noun, I'm OK with using "a lot". After the noun, you should use "alot".
"I like that a bit." "I like that a great deal." "I like that alot."
Spot the odd one out!
As I said - no issues with people using it, fine, don't mind, as long as it's not in a professional capacity. If I can say "alright," you can say "alot." Wouldn't be my choice, but a-okay by me. It's not
correct though.
That is - if there is such a thing as correct! I might not like the word I'm about to cite, but if you'll excuse the nepotism,
irregardless is officially recognised by Webster. Words are catalogued by usage, and alot gets a lot of usage - but "a lot," certainly, is both widely approved and deeply consistent with the rest of English grammar.
...If there is such a thing as consistent with English grammar.