Thank you very much for the screen cast illustrating the problem. I noticed that your palette is "floating". First thing to try is docking the palette back into the main yEd window.
If that does not help, you will probably have to create swimlane nodes by copying and adjusting existing swimlane nodes. To do that, open one of the swimlane examples from "Help" -> "Example Graphs" -> "Swimlane", select the swimlane node, copy the swimlane node (using COMMAND+C), and paste the copied swimlane node (using COMMAND+V) into your current diagram.