"Periodically" could mean once every hundred years. Without the text stating what the period is, it could be anything. The "consumed and destroyed utterly" phrase means that PCs have less than a day to rescue the soul of an imprisoned character.
There is also nothing in the text that indicates that the amount of activity the lich does modifies how often he has to feed the phalactery. In fact, the term "periodically" strongly implies a consistent rate, not a sporadic one. So I would use a different interpretation than others here and say that whatever rate the DM decides, it probably should more or less stay that way.
There is also nothing in the text that indicates that the amount of activity the lich does modifies how often he has to feed the phalactery. In fact, the term "periodically" strongly implies a consistent rate, not a sporadic one. So I would use a different interpretation than others here and say that whatever rate the DM decides, it probably should more or less stay that way.