It was the third.
LOL (also written lol and any other combination) is a common element of Internet slang used, historically, on Usenet but now widespread to other forms of computer-mediated communication, and even spread to face-to-face communication. It is an abbreviation for "laughing out loud" or "laugh out loud". "LOL" is one of many initialisms for expressing bodily reactions, in particular laughter, as text, including initialisms such as "ROTFL" ("roll(ing) on the floor laughing", a more emphatic expression of laughter, and "BWL" ("bursting with laughter", above which there is "no greater compliment" according to Magid. (Other unrelated expansions include the less common "lots of luck" or "lots of love".)
The list of initialisms "grows by the month" and they are collected along with emoticons and smileys into folk dictionaries which are circulated informally amongst users of Usenet, IRC, and other forms of (textual) computer-mediated communication. These initialisms are controversial, and several authors recommend against their use, either in general or in specific contexts such as business communications.
The use of LOL to express laughter is unrelated to other uses of the abbreviation, many of which (such as "lots of love" predate the Internet. LOL has also superseded the more-obvious "Ha!" that letter writers used to use