Does destroying a Lich's phylactery destroy the soul within it?

Question

The MM entry for a Lich mentions destroying a phylactery is a difficult endeavor but the only way to prevent a Lich from rising again and again.

Does destroying the phylactery destroy the soul within? If not, is there existing lore explaining what happens to a Lich's soul when its phylactery is destroyed?

Lich phylacteries in general can permanently destroy or consume souls fed to them by the required ritual, but presumably the Lich's soul is not one of them so long as the phylactery is intact.

D&D 5e answers preferred, but mechanics and lore from other related systems will be noted for guidelines if nothing in 5e exists on the topic.

Answer 1

No

The simple answer is that destroying the phylactery does not destroy the soul contained inside it, because no game rule in D&D 5th edition asserts that it would.

The lore in the Monster Manual, p.203 suggests that the phylactery is not necessary to protect the soul from injury, but rather to prevent it from passing to the afterlife:

A lich is created by an arcane ritual that traps the wizard's soul within a phylactery. Doing so binds the soul to the mortal world, preventing it from traveling to the Outer Planes after death.

Destroying the phylactery doesn't kill the lich, but only makes it possible to kill the lich, since with the phylactery intact, a slain lich simply re-constitutes at their phylactery:

When a lich's body is broken by accident or assault [...] within days , a new body reforms next to the lich's phylactery [...] Because the destruction of its phylactery means the possibility of eternal death, a lich usually keps its phylactery in a hidden, well-guarded location.

What exactly happens to the soul when the phylactery is destroyed is a mystery (see my answer to Can a Lich create a new phylactery?).