Lich dies, then Phylactery destroyed.

I know if the lich is ‘killed’ but the phylactery on the same plane, the lich can reform in 1-20 days. Also if the phylactery is destroyed while lich is still around, it is vulnerable to permanent death. My question, if the lich was ‘killed’ and then the phylactery destroyed, does that also just destroy the lich? Or is the spirit/soul still free to reform?