The ancients per my passing limited knowledge appear to be more concerned with the fortune of the physical being of the native when addressing this lot, rather than the modern use of this lot as the lot of financial/career/whatever success and old fashioned luck. I would be pleased to know my modern friends approach to the non planetary device.

Lot of Fortune was regarding as "Lunar Horoscope". Ancients called the Ascendant 'Horoscopus".
It seems that for the Hellenistic astrologers the Moon was representative for the Body (the physical body) and later on the meanings of 'Soul' were added to 'her'. Valens says that the Moon represents the Life (and the Life is connected to the physical body).
Lot of Fortune as a derived or probable secondary Ascendant has a lot to do with the physical body.
Later on, Bonatti says that if we want to see the state of the native's wealth and money in the following period we should direct the POF:

?But the Part of Fortune is directed for knowing the wealth of the native,
the increase of his monies, and his acquisitions."

So, I would say that ancients used POF for both purposes:
1. To know the well being of ones general health and the state of the physical body, and
2. To know the wealth and increasing in money and possessions as Bonatti says.