The word lying implies that Reuters was aware, either before or after publication, that their information is untrue, and they published that false information purposely and failed to correct it.
On that basis, it doesn't seem like Reuters is lying. It seems like Reuters has been accused of lying, by someone with a history of misunderstandings with the truth.
It may be the case that they have lied. That would be a pretty egregious act by Reuters. It may also be the case that Elon Musk has reason or incentive to cast doubt on the story whether it is true or not.
On that basis, it doesn't seem like Reuters is lying. It seems like Reuters has been accused of lying, by someone with a history of misunderstandings with the truth.
It may be the case that they have lied. That would be a pretty egregious act by Reuters. It may also be the case that Elon Musk has reason or incentive to cast doubt on the story whether it is true or not.