Like I said, they could be seen as friends or pokemon + trainer combo (or Pokemon + partner combo, as the Pokemon themselves call it). Nothing about enslavement, though there is definitely a power structure at play there, no matter what terms you use for it. Hence the "boss" term.
On page 707, Darkrai made it clear WHY he was willing to forgive Lovrina so much and WHY he referred her as his "partner". He wasn't anywhere near as desperate to please Lovrina compared to Victini, but he still wanted her affection and attention, regardless. Especially, when even the Pokemon feared and despised Darkrai so much. Partly because of his nightmare skill/curse, and partly because of all the crap he'd done in the Mystery Dungeon game this comic is based on.
It has been stated multiple times, both in anime and games, that the bond between a human and Pokemon is comparable to that of a parent and their child, or between two friends. Or that's what it's SUPPOSED to be like, ideally. But of course, we have groups like team Rocket who only treat Pokemon as tools.
It has also been hinted that many Pokemon WANT to have a human partner, even if they're initually suspicious about the person who captured them. For example, in gen 4, one of Dr. Footstep's translation about your Pokemon's feelings goes like this:
"<player> is... A remarkable human and Trainer. That I can always perform the best any <Pokémon> possibly can... I attribute that entirely to my partner <player>. When we travel, I can see wild Pokémon eyeing us enviously..."
Mewtwo had this dilemma for quite a while: his natural need for human's companionship versus his fears of being abused, like before, and being treated as a lesser being. That's why he reacted so strongly, when the one person he finally WANTED and TRUSTED as his partner agreed to it.
Now Darkrai faces the same dilemma, in a way. Part of the reason he probably called Lovrina his partner is simply because she captured him. Unfairly perhaps, but still. But more importantly, Darkrai still seems to crave for human companionship, same way Mewtwo did. He clearly had high hopes and plenty of loyalty for Lovrina at some point, but unlike Victini, he became disillusioned with her.
So now, instead of holding onto formalities and his broken dreams, Darkrai should stop viewing Lovrina as his partner altogether. If he still wants to have a human partner (and it definitely seems like it), he could ask Jen to be his partner instead. That way, she would be his parental figure/boss who’d treat Darkrai with love and respect. Instead of seeing him as a science project or a tool.