If I speak Loshon Hara under my breath so that no one else hears it but me (and Hashem of course!), is it the same issur?
Speaking לשון הרע which does not actually get heard can be likened to someone to desires to commit a sin but then is thwarted by someone or something. Strictly speaking, the Torah prohibits actions rather than thoughts. However, most Torah commentators (Ibn Ezra, Sforno, Malbim, Hertz) treat lusting to sin as a weaker form of commiting the sin itself. And of course, it is viewed as something to be avoided. However, this assumes that the person willfully intended to commit the sin, which in your case is speaking slander. It would seem that if you accidentally spoke לשון הרע under your breath AND no one else heard or even saw you forming words, then by the letter of the law you are guiltless. This would be similar to someone who almost commited a sin by accident. Even if it had happened, he could repent, but he need not do anything.