Lucian item question

What the benefit of taking Shiv + BT over Yomuu's + BotRK?

I've seen both used before and I've played with both but I don't really know the benefits of one vs the other as I haven't played more than a dozen or so games as ADC.

Also why doesn't anyone get trinity on him anymore? I see more and more people just not getting it on several ADC's including Lucian.

Thanks