I like the idea of overhauling Bloodlust since it is extremely strong for the builds that BMs generally run. This would especially help with new promos inevitably favoring strength builds, which BMs currently lend themselves very well to, in large part thanks to Bloodlust.
However, I'm not sure the energy regen is a great idea on the whole, at least not in the form you suggestion. Sure it would help BM diversify its builds, since Parasite is an underpowered energy regen skill comparatively, but gaining energy with every attack on top of that seems a bit too strong if you have lifesteal as well.
Let's say that over the course of 4 rounds, a Focus 5 BM deals about 800 damage (which is definitely possible with a Plasma Cannon/Robot combo). At a 14% conversion rate, that's an extra 112 energy and HP. Definitely not as much HP regen as Bloodlust currently gives, but 112 energy could be game-changing, especially if you use Parasite on top of that. BM could potentially become the class with the best energy-regen class in the game, which isn't exactly a good thing since it already has tremendous damage output as well. I gave an example for Focus 5, but imagine what str/supp could do, and that build relies on cores, which cost less energy than skills.
Overall, I definitely think nerfing the HP regen percentages on Bloodlust is a good idea, and that you need another effect added as compensation, but I don't think direct energy gain is the right choice. Maybe make it a more defense-oriented skill to help Focus builds out. Also, as RaXZer mentioned, this obviously needs to be a change specific to BM's Bloodlust, without affecting BH's.