With some of the most calm and rational interaction seen on the show so far going on between the two groups, and the good will act / actually giving some of the Lucian Alliance people names; it's looking like they'll join up with the destiny crew, if only for a few main important members and some redshirts to slaughter when introducing new enemies or problems. My guess: Right before Young makes his move, whatever caused that guy to burn up will make itself apparent, and everyone on-board will go "Oh snap we'd better all get our shit together and stop fighting each other before we get turned to charcoal". Eli will find some magic device down in the bowels of the ship and reemerge to save everyone, then someone will give a hurp durp speach about working together to survive on the ship.
All the civilian / military tension and pointless bickering will stop and shift over between Earth crew / Lucian Alliance crew, who will cut out the bullshit by just threatening to kill people when there's a conflict. With multiple alien aggressors they'll all have to be on their toes, and with pushing from the LA they'll explore more of the ship looking for defensive systems, leading to more cool discoveries and alien encounters, rather then just finding the Kenos and that coma chair and calling it a day.