As I understand it, Broken Lords not only can feed without draining the life of others but also don't truly understand all the merits and drawbacks of draining at the start of the game. In lore, it appears a Broken Lord called Lacebranch first found out about draining life a little while before the game is set. The first missions have you researching technology to understand it better. Draining life is always shown to heal the drainer and hurt the drained, as demonstrated by all of the broken lord's units having some heal after attacking. Dust bishops effectively heal others after attacking implies that this is a skill that broken lords can learn and use to recover. As the Broken Lord questline goes on, they learn how to master this and use it to their advantage. It is mentioned in a hero bio that Broken Lords extend their life by draining (implying Broken Lords are in fact mortal) and that Broken Lords are considered outcastes for draining.

There is reason to believe that being drained like this is not always fatal. In friendly villages, Broken Lords allow the inhabitants to give penance by allowing themselves to get drained. At the end of the Broken Lord questline, they learn how to build temples that can feed off all the inhabitants of Auriga, presumably without hurting them (this appears to be the building in the middle of every Broken Lord city).

The Broken Lords are never said to be able to extract dust with this ability. It seems that they can only consume it. Dust efficiency is described as an ability to sense dust, and dust from battles comes from Broken Lords recycling their dead soldiers.

What I will say, however, is that the amount of dust to heal a single unit or hero is substantial. A single hero or unit can easily take the income of a small city over several turns to heal. This would imply draining a single person is the equivalent of draining the output of many people collecting dust for days.

Draining is often described in the main quest as making the drainer feel more powerful. There are two artworks of Broken Lords draining they show two different Broken Lord heroes draining with their left hand (which is always shown to glow on Broken Lords), their targets appear to be unable to move much and alive, which leads me to believe the dead cannot be Drained. Importantly Broken Lords get a hero skill that allows them "though an act of pure will", infuse their soldiers' armour with dust from themselves, implying that they can control the dust they drain to a large degree.