I have tried it, but I can still spam the button to deplete my character's health. Did I do something wrong?
Yep that's wrong.
On the button click event condition, add the condition 'var = 0' to the same event block on the left, they are called conditions.
Where you have the first action set Anim_Lock to 0, change this to 1
Where you have the set Anim_lock to 0 action further down next to MyUID, delete it.
The on animation finished event should be on its own, not inside the button click.