If you're being especially careful, you may want to stick with "aloud" in formal writing; but "out loud" is standard and even preferred in some sayings such as "laugh out loud."
If "out loud" hadn't become a rival of "aloud," the text messaging abbreviation could have been one character shorter: "LA" instead of "LOL" but I imagine "LA" wouldn't have caught on. Los Angeles and Louisiana would not have been amused.
Source: Grammar Girl