The barrier generation stat doesn’t seem to have any impact on barriers generated by the sorc passive that activates a barrier when using a cool down.
Tested using both an item that provides a bonus to barrier generation and the Lionheart malignant heart. First test was with no bonus. Second and third tests were with one of the bonuses each, and the final test was with both on.
In all cases, the amount of barrier generated by activating the cool down was exactly 30% of my health as stated in the tooltip. The amount of barrier generation my sorc had had no effect on the amount of barrier generated.
This makes the Lionheart malignant heart effectively useless and any barrier generation bonuses from skills, paragon, or item affixes useless as well.