You only touch the surface - you're talking about what's going on
in that instance. A pirate lord shouldn't be a single fight - it should be a series of fights. Perhaps you come across his lackeys attacking a trader, and you kill one. The other submits (becomes invincible for a few seconds), stops, and sends you a message. "If you're after our boss, we lasty heard from him in system X, but please, don't kill me!" You can then kill the pirate for a bounty, or continue onwards towards your target.
You arrive in system X. A passing trader or system security (RNG to decide) warns you to steer clear of celestial body Y - ships go missing over there. You, obviously, head right over there. For shorter missions, you meet the pirate lord. You attack him, bring him low on health, and he high wakes. perhaps, faster than a normal NPC or even player could/would. You track him.
You meet him in supercruise in system Z. You interdict him, and murder him. Maybe, if you didn't murder that poor lackey a couple systems back, he'll come around to help you (RNG roll decides whether he shows up or not). You go back to the employer, who pays back the mission reward and the pirate lord's bounty, in full.
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This could be iterated in a hundred ways. You could find a pirate base. You could incapacitate the pirate to allow security vessels to pick him up for trial. You could join him in his dastardly act and reap some of the benefits of the deed. Maybe, you'd even gain a contact, and he could become a persistent NPC whom you can establish contact with, and he could provide you with some minions for your own pirate quests, the location of a hidden pirate outpost, the whereabouts of a good mark, etc.
Then you have the other assassination missions, the illegal ones. That spiritual leader, that political scumbag? Potential contacts or credit vouchers, with their own chains, their own requests. Factoring in having to dodge the law could be very nuanced and fun. This is all before mentioning the plethora of other missions available. Personally, I'd like to see some love for piracy missions. I want my targets to mean something, and I want to have rep with other pirates.