The lawsuits underscore the legal risks developers of chat bots face when using troves of copyrighted material to create apps that deliver realistic responses to user prompts.
In December Twitter Inc, owned by Musk, suspended the ElonJet account, with the billionaire threatening legal action against the account's operator.
One element courts look at is whether a company made clear to employees that the specific information at issue was a trade secret.
Meta, which launched Threads on Wednesday and has logged more than 30 million sign ups, looks to take on Elon Musk's Twitter by leveraging Instagram's billions of users.
The launch comes after Twitter announced a slate of restrictions on the app, including the need to be verified in order to use TweetDeck.
Elon Musk seemed to enjoy his training sessions, commenting, "That was fun!" on the photos shared of his workout.
Elon Musk challenged Mark Zuckerberg to a fight after someone tweeted claiming that Meta is developing a Twitter rival called Threads.