I think it's interesting that Lilly's parents are never even a consideration for Captain Martin-this is someone used to throwing his weight around to the extent that he can.
He takes pride in being able to protect his men, acknowledges the risks of his actions, and has an aspiration of being remembered, with land and influence in a kingdom of Lilly's creation.
The hard part is telling if it's professional pride, or actual "father to his men" pride. Talking to the dead guy Tovak shows he has some regard for their deaths, and he can be polite to Yola, a woman working under him (his intentions for not saying Tovak was into her are questionable, though.)
Clearly, his goals show his actions are primarily rooted in self-interest. He wouldn't have stuck his neck out for Lilly a year ago, and he was going to let Lilly get taken by Lord Waters, if she hadn't reminded him of the other boy who got Tithed. Obviously, self-preservation plays its role in his decision-making.
Let's be glad he wasn't using {Lion's Paw} in the Waters confrontation. Or was he, and his neuroses just go that deep?
It does seem as though he's come around pretty quick on betraying the kingdom he's undoubtedly sworn to obey (having a dead wife and distant daughter probably help, he doesn't think of them once here), and just stuffs that down by telling himself "I only get one shot, this opportunity comes once in a lifetime". {The Ladder} says its because knowing Lilly is righteous does the trick there, but he only tells himself it's "icing on the cake."
The worse parts of him are angling to possibly marry Lilly, which could be a holdover of "that's how they roll in Narisell, you try to marry the highest power/status person you can, regardless of age or other factors." He also shows no real regard for all the lives the Watch undoubtedly saved with Lilly's help. Not standing on his laurels, maybe? Or so used to pushing off death that it doesn't matter to him?
All in all, a pretty mercenary attitude, with maybe a toehold toward being good. My guess is focusing on weighing out risk vs. reward is how he's survived this long, seeing as his Dungeon knowledge implies experience there, or contact with people who have beaten Dungeons.
What is so important in the east that Lord Waters would ignore the Dungeon to take Lilly with him to accomplish? Is Waters and his entourage tough enough to just disregard it? But then they could have just beaten those 17 Watch members and taken Lilly. Ugh, so many questions.
Edit: Risk-taking behavior is in his nature enough that I think there was mention of a roll for pushing to clear the [Rapid Iterator] after Heartbreak. He's ambitious, clearly.