Yes Scott Lobdell created the All Blades but no he didn't make Jason magical. That's a common misconception (*1.) The All Blades Lobdell created were retractable swords Jason could easily hide on himself. In fact the first time we see him get them he retrieved them from two ankle sheaths. The swords are magical, he has never been stated to be magical by Lobdell.
The All Blades are supposed to activate by the presence of evil and draw extra power when Jason cut himself with them. Which was when they had energy coming out of it. Lobdell only has Jason use them with the Untitled.
I think the concept might have been to build an arsenal for Jason to allow him the ability to fight different threats ? That's the impression I got with him using them and then alien weapons. But that wasn't touched when Lobdell returned.
The sixth panel shown is from Jason's coma after the Joker burned his face. He has the glowy patterns that were painted on for his All Caste test. Whatever abilities he has is moot because it's a dream.
Tynion came onto the title and didn't know how Lobdell wrote a lot of things. There was literally no explanation for why Jason's chest glowed (again that only happened under Lobdell in a coma dream) and why he could now draw the All Blades from his body. Roy asks about the marks, never gets a real answer and it's never questioned again.
Greg Pak was told the guns were gone in favor of the swords and dubbed them "energy swords." He had Jason use them on foes that weren't supernatural and fighting Supergirl who isn't evil. I'm not sure if Pfeiffer had Jason use an All Blade or just a katana. In the Pfeiffer comics themselves I can't recall him doing anything with it.
*1 Lobdell has hinted at Jason having different abilities but it has nothing to do with the swords and could be explained by other means.