If you care to click
here,
WaldoMF, the link will take you to the appropriate page on acronymfinder.com - supposedly the most comprehensive list of these things on the WWW.
There you'll find it offers 'laugh out loud' and 'laughing out loud', just as I suggested earlier. At no point does it suggest that it means '(I) laugh
ed out loud'.
Were people to write ILOL, as I have just hinted, it would be perfectly sensible, but they don't, so I maintain that LOL is absurd or untrue.
That doesn't make me defensive about acronyms...people are more than welcome, as far as I am concerned, to be as idiotic in what they write as they choose to be. I responded as I did purely in response to the question here.