It IS possible, but only in one a bit hidden way. First I'll tell you about the alternative ways:
- you have a conceptual error here. Timelines in Sequence diagram are not classes, but objects. So, they can't become classes.
- Of course, a tool could have a function to create a class according to an object, as VP UML has. Obviously, EA has not such feature.
- On the contrary, it is not a problem to drop a class on the sequence diagram to become a timeline. But EA has some conceptual problems with it, too. You have to make it an object here. Look also this.
- On the other hand, there should be no problems to drop a timeline to the object diagram, but in EA it IS a problem - the object-timeline remains the timeline even on the Object diagram. That is obviously non-convenient and ununderstandable, but it is so. Obviously, it is one of these bugs that are called "features".
- The same is behaviour of the timeline if we drop it on the Class Diagram. We even can't connect this object to a class by generalization - EA considers such connection as a rules breaking one.
And finally, how you CAN connect the timeline/object to a class. Right-click the timeline on the sequence diagram or its copy object on the class diagram. Go to Advanced. Choose Instance Classifier - the first menu item. There you can choose an existent class or even create a new one. And the object/timeline will belong to this very class.
You can't reach this feature from the Project Browser. It is obviously, another "feature" of the EA.