A EDH deck I am wanting to build revolves around Lich's Mastery. I'm aware of the removal that may occur to it and that I can Stifle the ability of When Lich's Mastery leaves the battlefield you lose the game. I know Deflecting Swat can redirect an ability on the stack and Lich's Mastery's last ability goes on the stack. Can Deflecting Swat redirect Lich's Mastery's lose the game ability?
When Lich's Mastery leaves the battlefield, you lose the game.
That ability doesn't use the word 'target', so you can't redirect / deflect it.
115.1d A triggered ability is targeted if it identifies something it will affect by using the phrase “target [something],” where the “something” is a phrase that describes an object and/or player. The target(s) are chosen as the ability is put on the stack; see rule 603.3d.
No. Cards like deflecting swat can change the target of spells and abilities. For that to work the spell or ability will need to have the word target in it like Lightning Bolt says "Lightning Bolt deals 3 damage to any target." Lich's Mastery does not have a target, it simply has effects that work on whoever controls the enchantment.
In order to do what you want you would need something like Harmless Offering at instant speed, to give an opponent control of Lich's Mastery before the destroy effect resolves.
No, this will not work.
The triggered ability of Lich's Mastery does not have a target, and Deflecting Swat can only change the targets of spells and abilities.
Lich's Master affects “you”, which refers to the controller of the ability. It does not affect “target player”. An ability is only targeted if it uses the word “target”, or if it uses a keyword that has “target” in the rules text.