I have to correct that a little bit
They did in fact originate online. They existed long before phones were capable to send txt messages. As a long time "Onliner" I've been around since the times of BBS, before the internet as we know and use it today existed. Messages have been exchanged through networks like the famous FIDO Net, and the likes. Even back then, abbreviations became custom. They were basically born for a similar reason, like they are used on phones. To shorten the messages.
Back then all data transfer happened via dial up modems. It started as early as the usage of acoustic couplers have been the hardware requirement for data transfer. They've operated with 300baud. Transferring messages took forever. Several megabytes took hours. Hence the abbreviation lingo was born.
It remained that, during the times of IRC, and AOL chat rooms, which at that time have been the two largest platforms on the globe.
Real time chat also had a need for quick response. A busy chat room with 20+ people communicating in real time required a fast way to get a message through.
And that's why we have abbreviations, and internet lingo.
Over the years it persisted and evolved. That evolution tho isn't really that dramatic. In a way it became a bit dumber, since it lost it's initial purpose and meaning.
Much of what today's lingo consists of is also but a remaining of the gone days of software pirates. Those were the ones for example who started to change the spellings.... From Software - to Wares - to WaReZ, just to give one prime example.
All in all.... Today's internet community hasn't added too much new things. Most are around longer and older than the users who are using the lingo.