dude got his collarbone nicely cut and was still able to use his hand, cuz he healed that quickly. those bozoes pursuit would only result in their death.
Is that how it works? I remember seeing a video of a guy born without collarbones and he could use his hands just fine; its main purpose is shoulder stability and strength but it probably won't prevent someone from using and raising their hand, though I assume it's really uncomfortable and painful to do so.
In any case, I don't think he healed before raising his hand. It seems that magic activation is visualised through the sparkles; we can see in the panels how he puts his hand over his wound and then the sparkles happen. So the way I interpreted that was that he had to raise his hand and lay it over his wound in order to apply the healing magic.
Also, in general, the activation of magic is shown to come from the hands (which may be a habit from using wands and the hands just generally being dexterous which may be a factor in manipulating magic).
So either the collarbone hadn't been fully sliced through, and it was just a flesh wound (still lethal considering the amount of blood that would leak out), or being sliced through didn't actually impede raising his hand. I'm inclined to agree with you that it's depicted as being nicely cut, but on the other hand the cut was done with a very short and light knife so I wouldn't be that surprised if it just slid over the bone, not truly slicing through it.
Despite what Lucas said about the wound "healing instantly", it seems to be incorrect since, while fleeing, Quintus was shown to still be holding his hand over his wound so clearly it hadn't fully healed.
As for the guards pursuing Quintus, I wouldn't underestimate a group of organised people surrounding a single person who is already wounded and has one arm occupied. More importantly, since Lucas managed to get the upper hand over Quintus, and Quintus clearly was alone since no one joined him during the ambush, he could have pursued and apprehended him. Besides, if the expectation is that a group of people who aren't as powerful as the duke can't capture Quintus, then I question his decision to go give orders to the garrison for countermeasures against Quintus. What are they going to do?
So yeah, the only way I can rationalise Lucas' decision not to pursuit is that he was worried about traps (Quintus cut some rope while fleeing and was also throwing smokescreens). But hey, group of guys on horse versus fleeing wounded guy on foot who I doubt set more than a trap (his aim was to ambush rather than lead in traps). It seems that they had the ability to absorb some risk and capture a dangerous criminal.
In the end, I was not impressed by the passivity or cautiousness of the decision to drop the pursuit. Then again, perhaps it is something we should have expected; after all, Lucas had expressed before that one of his status should always perfectly win so it may well be that avoiding anything that carries any risk of failure, or any appearance of it (such as any scar), is his nature. (Recall that he considered Roy's intervention against a monster to be a stain on his family's name.)
We'll just have to see how his personality gets fleshed out in the future.
Roy is, of course, a regular protagonist; although he is cowardly, he may take far more risk.