The templates say it "loses its tiers (and all abilities from those tiers) and gains abilities from the mythic lich template, according to the base lich's CR."
What happens when applied to a Mythic character with a Path? Do you loose all your path abilities, such as the Archmage Arcana or the various tier powers, or do you just loose the base abilities such as Hard to Kill or Amazing Initiative? Or something else?
You lose it all. Every ability from a mythic path, including base mythic abilities, is replaced by the template.