LOL is an English slang that represents the abbreviation of the expression "laughing out loud", and in Portuguese it means something like laughing out loud, rolling with laughter, etc.
Other people ascribe different meanings; a possible variation is "lots of laughs". It's a term used a lot on the internet, and it was initially created in multiplayer games.
In addition to the English meanings, for many internet users LOL can also mean a person with arms raised, to commemorate or celebrate something that happened, and it's a widely used emoticon too.
More and more expressions and slang in English are becoming more popular in Brazil, and LOL has already become a fever among teenage slang.
League of Legends
Another possible meaning for LOL is League of Legends, an online multiplayer game with millions of users. The game has become so popular that several tournaments are organized, and some people make the game their profession because they manage to earn money through it.