Fix for Diablo 3 lag coming in future patch
Diablo 3's Reaper of Souls launch has been going much more smoothly than the first couple months of the original game. That said, there are still some annoying lag issues which persist. Personally speaking, I've seen both these happen, although they seem to happen intermittently for me at worst. There have been times where I've played and not seen them at all -- but nonetheless my ears perked up when I heard Blizzard has a fix incoming for them.
As Omrakos explains, the two lag issues being fixed in particular are...
"Also, loot drops and it's not displayed for several seconds"
There isn't a timeframe for the patch, so I wouldn't hold your breath. But one has to imagine it's soon.