If we are to make healing happen, we must consider the following:
-Healing must not allow for knights to sit around and heal. We're not making love puppies on wagons.
-Healing must come at some kind of cost, and must leave existing strategies viable.

Idea number one: Vampirism+Nerfed health

Make it risky and weak for such a great buff. I'd say something like an addition to the cautery line that goes to 5* or a new cutter, and has "healing properties", but at a cost. Something along the lines of:

"Improved cautery sword" (Or whatever it's base weapon type is; although I think a gun would be going too far)
[Relatively low normal damage in comparison to other options]
[Steals health from enemies on charge; gives 1/2 a heart to a random party member tops]
[Long charge time, with meh damage]
[reduces health by 50%; or 2-3 bars of health, perhaps per tier]

This would make it risky and hard to use- kind of like chaos cloak. It'd prevent the farming of HP, and would make it only useful in truly awful situations- but in those situations, it could save the day. It'd also make it fair (but not really viable, like 90% of the other weapons...) for lockdown, as strikers using such a weapon would have to only use the charge. It would not interfere much with the current levels being farmed by T2 and T3 players as it would be a small bonus that didn't make it go much faster than it currently does.

Idea number two: Luck

Make it an armor or shield buff. Make an "arch of aorta" type shield, or a vitasuit amazing. Such an armor would look like-

"Amazing shield of finding hearts!"
[Low normal defense]
[+1 stage of 'luck' (marked with a heart)]
[-2 stages of global damage; -3 stages of resistance against X]
[Misc. status bonuses here]

'luck', or whatever OOO wants to call it, would increase the chances of finding hearts, but not by much. This would make it a nice passive bonus for parties of newer players, or players attempting dangerous content like shadow lairs where finding no hearts for prolonged periods of time could be fatal. Of course, this does interfere with existing strategies, so how can we make it viable? By giving the players using the "amazing shield" a terrible shield. It'd be like swiftstrike, except it would be more stable and would hurt the player's damage and thus abilities to effect enemies. An interesting scenario.

*as a side note, this is just what I'd do if I were to make a healing effect. I'd much rather see OOO make new enemies for the normal, main game, than another knight buff for me to collect.