Does every tradition, especially ones descended from the lotus sutra and the Buddha's immeasurable life, claim that parinirvana is a conventional existent?
Assuming that it's not a dharma, I don't know.
In my experience, zen and tibetan buddhism do not claim that the self of an enlightened one can be completely non existent. In fact a zen master when asked this question might answer "Uncertain." or "yes" or "no". Ask for definite answers is a limiting factor in an unlimited universe.
The following article discusses your question in far more detail than I can:
Here is an excerpt that applies to your question: But there is no doubt that they affirmed the reality of the self or person, and that with scriptural authority they held that the self of an enlightened one cannot be described as non-existent after death, in “complete Nirvana” (Parinirvana), even though the five “aggregates” which are the basis of its identity have then passed away without any possibility of recurrence in a further life. These five are material form, feeling, ideation, mental forces, and consciousness.
It seems, then, that they thought of some aspect or dimension of the self as transcending the aggregates and may have identified that aspect with Nirvana, which like most early Buddhists they regarded as an eternal reality. In its involvement with the aggregates through successive lives, the self could be seen as characterized by incessant change; but in its eternal aspect, it could be seen as having an identity that remains constant through all its lives until it fulfils itself in the impersonal happiness of Parinirvana. Although their account of the self seemed unorthodox and irrational to their Buddhist opponents, the Pudgalavādins evidently believed that only such an account could do justice to the Buddha’s moral teaching, to the accepted facts of karma, rebirth and liberation, and to our actual experience of selves and persons.