In the Animation event sheet, your idle animation overrides the Lightsaber almost immediately. I added the condition in bold after else in the else event to get it working, though the animation is too fast in this mock up.
+ Player: is walking
-> Anakin: Set animation to "Walking"
-> Anakin: Set animation speed to 20
+ System: Else
+ MouseKeyboard: [negated] Player 1 "Action" is down
-> Anakin: Set animation to "Idle"
Depending upon the desired behavior, you may need to make the conditions a bit more complex. I haven't worked with animations much, but I found it puzzling that I couldn't get the 'On animation playing' and 'On animation finished' conditions to work (I set the Lightsaber animation so it wasn't looping.) Not sure what that's about... I'll have to try that again later.
You may notice that I used [negated] Player 1 "Action" is down above to keep the idle animation from overriding the Lightsaber animation. I replaced the 'Key Enter is down' below (in the Lightsabe events) with an action check as well, as it's a bit more friendly toward changing controls and such that way.
+ Player: is on ground
+ Player: Value 'canslash' Equal to 1
+ Player: [negated] is moving
+ MouseKeyboard: Player 1 "Action" is down
-> Anakin: Set animation to "Lightsaber"