From what I've seen, Xayah is good at kiting. She can be 1v4 and get a quadra so long as she kites and uses her combo properly. If she's chasing someone though, she loses a ton of damage.
Rakan is good at set ups. His knockup and ult can put people in one area and let his ADC combo off that.
So, for Xayah to be good with Rakan, Rakan has to hit his knockup and Xayah has to quickly use her Q, auto, W, auto(s), E combo to either burst or keep them locked down long enough for Rakan to do more lockdown (don't know his cooldowns yet cause I haven't played him).
The really strong part about them though is they get a ton of damage from Xayah's W. Extra attack speed plus 20% more damage per auto and bonus move speed if used against champions for BOTH champions and it works on structures.
As far as what they work well with, Xayah wants someone to keep people in place and Rakan wants someone to do damage while he locks people down. Anyone who can work with those ideals will work with either champ.
Morgana's snare gives Xayah tons of time to set up a combo, same with Thresh, Blitz, Nami, etc.
And as you pointed out, Rakan is good cause he can either start a fight or join it. Either Rakan starts the fight with knockup and Lucian follows up with combo and gets shields after, or Lucian E's into a fight, Rakan can shield him, knockups the enemy, and then shield Lucian again, giving a ton of protection for a short range ADC and giving Lucian time to combo regardless of which order the fight happens in.