Normally the only way you are supposed to get civilians as ship lieutenants is when you complete a quest for an NPC and when you are done talking to him/her there is a chance you will get a dialogue option to ask said NPC to join your crew. The civilian may or may not accept your offer. But Ubisoft overlooked one thing: If you knock out characters from random quests you'll have the option to recruit the manual way (haven't tried this with story based characters). I've looked up "recruiting civilians" online and couldn't find any reference to this, so I'm assuming it isn't intentional.
So what is the purpose of recruiting civilians? Most of them have common perks, so it's just if you're tired of using the usual soldiers and mercenaries and rather would have unique looking allies.
In the first example I come across a civilian from whom I can start a quest. Both her and another civilian in the area are quest generated and are available for recruitment. Because I don't have the option to knockout, I just deplete nearly all their health and finish them off with a non lethal Sparta Kick (make sure they aren't taking poison/fire damage during this or they can still die).
Next example I accept a mission where I'm assigned to kill a character. What I do instead is knock her out and recruit. The game counts that as a kill.
Last example is a quest to protect someone from attacks. I did this mission twice to see if the game randomizes characters' appearances, and it doesn't seem so. One of those times I recruited her before the quest was completed, resulting in a failed quest.
At the very end I show the recruits on ship and with the Call to Arms ability, where I make some observations. On ship you see them standing in the middle (two of them were from another quest I had recorded but cut to shorten the video). The game gave them each a sword, but when I use the Call to Arms ability the civilians go back to being unarmed.
I've been keeping an eye on possible unique recruits from quests and found one in a Ubisoft Club quest called the Blind King (renamed Prince of Persia The Blind King ingame). Description in a spoiler tag for those who have not yet done the quest.
Upon recruiting him you'll find out his actual name, Assassin. What's unique about him besides his name and high tier stats is that he may be the only Persian that can be recruited (only other time I can recall facing these soldiers is at the beginning of the game while playing as Leonidas). Only setback is if you choose to summon him with Call to Arms ability the game won't spawn him.
I also tried recruiting Artaxerxes, but alas, the option never appears.