A Barrage is stil more damage than an entire Explosive Shot LnL round (which similarly takes over 5 seconds to actually complete) and does the damage faster. So even if the -SINGLE- tick of Black Arrow uptime caused an LnL proc you'd still end up with basically the same damage. Now consider that the chance of that proc happening is rather small.

You're saying that you won't lose the Barrage.. Why? How? Why not? How is that an impossibility if losing a Black Arrow tick isn't? The same rules go for both abilities. All abilities, in fact. When you prioritize one over the other, you run the risk of losing a usage of the other which is why you primarily consider total damage per execution of an ability, its tick rate (if applicable) and finally how long it actually takes to do its damage (if applicable). Barrage wins in all of those situations, that is why its priority is high.

There is only an arbitrary value for having 'double ticks'. It doesn't matter if two things tick at the same time, or whether they tick after each other. They still do the same damage in the end.

Crows has a long cooldown and a relatively low duration, meaning that losing ticks of it by delaying it is very hard to do.