I grabbed a copy of the Quick-Start-Guide, June 2022 of the game, and its Charsheet features "LCK" in the middle between the standard d20 attributes:
This shorthand is not referenced anywhere else, but it is talked about on page 1 of the Quick-Start Rules, which implies that the Abbreviation LCK stands for Luck:
- The Bloodlines & Black Magic Roleplaying Game uses
seven ability scores (instead of six), adding Luck as an
ability score to the traditional six: Strength, Dexterity,
Constitution, Intelligence, Wisdom, and Charisma.
The page also says something about compatibility (emphasis mine):
The original edition of the Bloodlines & Black Magic Roleplaying Game was designed to be compatible with the first edition of
the Pathfinder Roleplaying Game.
This edition of the game has instead been designed to showcase its compatibility with the 5e-version of the d20 system. We hope
that, with this PDF, players familiar with other 5e or d20-based games will find learning to play the Bloodlines & Black Magic
Roleplaying Game more enjoyable. Players familiar with 5e-based games should note the following: [...]
So, the QSG is for dnd-5e.
LCK is retained on the official char sheet
The official character sheet is the same as in the quickstart rules, so again, it would mean Luck. It is thus also for dnd-5e.
Is it an Edition conflict?
There are currently two different Editions in existence, as far as I could find out:
The two games are totally separate. The whole game was rewritten from Pathfinder 1e to D&D 5e, as page 2 of the edition for D&D 5e tells (visible in the sample file) with emphasis added. In fact, that part even implies the two are not fully compatible:
Within weeks of releasing the original version of Bloodlines & Black Magic, individuals immediately began to ask — can we get this in 5e?
For well over a year we spent days and nights working on conversions, all while trying to ensure that we didn't lose any of the elements that make Bloodlines & Black Magic what it is; at the end of 2019 we decided to write this as its own game.
Bloodlines & Black Magic uses the OGL but has otherwise been redesigned to accommodate the setting in which we want to play.
Whatever version you own, the character sheet belongs to the exact other version, as do the Quick-Start rules. And since the Quick-Start belongs to the dnd-5e edition, you own the pathfinder-1e edition.