Kuzan was a broken man; it is interesting to notice that he's, as far as I recall, the only admiral whose justice changed: he used to defend a burning justice but after Ohara he changed to the lazy justice we all knew. This passive approach to life was stressed by Jinbe when he explained that Sakazuki and Kuzan fought to become Fleet Admiral: he said Kuzan rarely showed any motivation for anything but didn't want Sakazuki to become the Fleet Admiral, which is interesting because didn't sound like Kuzan wanted the position for himself but simply didn't want the psychopath he witnessed at Ohara to rule the Marines. Is a reactive approach that, again, fits the profile of a broken man that simply exists as a passive observer of the world —in this case, Kuzan acted out of reactivity, not proactivity. Hadn't been for Sakazuki being nominated I doubt he'd have went for the position.
When Blackbeard met him at the bar, Kuzan again emphasized how broken he was and mumbled about Saul, Robin and Ohara. This is clearly the key for his game: as of now he isn't a lost man but has a goal, a determination (as noticed by Doflamingo), and this determination should be related to understanding what happened in Ohara, why he had to "murder" his friend and what justified Sakazuki to annihilate civilians like that. In other words: he needs to make sense of what broke him in the first place, and that must be why he allied himself with the D. who is into archaeology and who offered him a vehicle to seek his own agenda.