It all depends on what the contract he signed says. And apparently the band has a zero tolerance policy for this kind of act while in contract with the band.
And if he finds fault, he could sue. But I guarantee he won't sue the band, because he knew what he signed. He should've known what this kind of act would cause if it did happen to be recorded and leaked, which it did.
He is doing the right thing by suing those who did leak this video out. They're the ones who did the defamation, not Dave. Dave and Megadeth were caught in a rut by Ellefsons decision, and the attention it caused for both Ellefson and the Megadeth brand.
And Dave is doing what is best overall for the band. As with any company, you (the employee), represent the company. Anything you do, especially in company uniform and on the job, is a representation for the company and it's image and reputation. When that customer walks in, you the employee are expected to give the customer the best service that best represents the policies and values of the company.
Here in this instance, Ellefson did not represent the company in a good light, and in turn caused a bit of a negative representation to the Megadeth brand.
That's how I see why Mustaine chose to fire Ellefson, regardless of legality of the action performed by Ellefson that caused him to be in the spotlight. And, depending on that contract he signed with the band as an employer, I feel Mustaine was in the right to be concerned for his Band and Brand of Megadeth. It was just a business decision that he felt was the best choice to make, regardless of feelings, and apparently there were already some mixed feelings already brewing.
And also, Businesses are only doing this as a reaction to all the outcry the MeToo movement has been very vocal and demanding about. It's why every business is disassociating themselves from their employees that are involved in this type of reputation caused by an employees actions. It also doesn't help when what you are employed for is responsible for the light that always shines on you. You are always under the spotlight when you are in a band, an actor, or in any Business/Industry where you can be Idolized and seen as a Role-Model.