Sad to hear your so many problems with this fig/breba.
it's not for sure a cold hardy variety.. it is right on the opposite side, Lampeira does good in hot/dry climates, with minimum rain fall. - may be not suited to your particular area
The great majority of the plants cultivated by small farmers, as well as in urban areas, on back yards and public spaces, are not at all irrigated.. many trees older than me..
I am convinced that a number of nurseries may also be selling the wrong plant...( thought that this could only happen here ?! )
Hopefully some of those scions you mention as originated - ..from 3 different Lampeira sources
-- Pon's, Greece & Turkish repository.- may have landed in California where conditions would allow a successful root/growing and soon we see those juicy brebas ripening there as well as its prolific main crop boosted by the little bug.
That tree in Vancouver producing a productive breba crop with blood red interior does not seem to be a Lampeira Preta (black Lampeira). The insides of the Lampeira's brebas are more like ..amber to light pinkish
Another Lampeira ( the white sister) also a two crop fruit but Common -not San Pedro- ok.. their figs are with light red pulps and if being pollinated may darken to strawberry red but not 'deep red'.
Have been searching various forums and discussions on the LP cultivar and for sure, IMO there is a good deal of confusion. May be DAVIS archives could bring some help once LP was registered there many moons ago under reference PI-18871 and apparently cultivated at Niles long time ago.
Francisco
Portugal