Can a Lich die of old age? Hear me out.

To understand how a Lich could die you have to first understand how a Lich can regenerate itself back from death. A Lich can regenerate itself after being slain because its soul does not inhabit its body but instead inhabits the phylactery. The phylactery is comparable to a body in that they both hold the soul and that when they are physically destroyed the soul is no longer bound to the body/Phylactery. The difference is, is that the body has an expiration date while the phylactery is an inanimate object, thus the Lich is seemingly immortal.
Basically a Lich's continued existence is based on the phylactery which is why it is very much mortal.
You see even inanimate materials, such as minerals, woods, and metals still have an expiration date in the form of corrosion,oxidation, radioactive decay, and biodegrading. Based off of what i have seen in Dungeons and Dragons a Liche's phylactery can be destroyed similarly to any item, therefore it must be vulnerable to things like oxidation, pressure, and energy.
What i am basically getting at is that the phylactery could be destroyed simply through natural process of disintegration. Now how long it would take for it to disintegrate would depend on the materials its made out of and the environment its kept in. For instance if your Lich's phylactery is made out of parchment and lets say the Lich is complete dumb ass and keeps it hidden at the bottom of a lake than it would probably have the life span of a couple months. alternatively if your phylactery was a rock and you stored it in a protective environment, than the Sun would probably die before the Lich would.

While Phylacteries are usually magically protected in some way, that protection usually just entails alarming the Lich if its phylactery is in danger or its a curse that becomes inflicted on you if you attempt to destroy the phylactery. Neither of these protections properly protect it from the passage of time at least not to nearly the same extent that a good coat of wood finish or vinegar would. I recommend that DMs keep in mind that a Lich should return to their phylactery every 2 to 3 weeks to maintain them from corrosion. If a Lich has a phylactery made of wood it would be preferable that it re-coats the lacquer, if its made of metal than it could use baking soda however it would be preferable for the purposes of D&D lore congruity that your Lich use white vinegar instead.