Does Sivir's Boomerang Blade do damage on its return if you die after activation?

Solution 1:

Yes, Sivir's Boomerang Blade will finish its animation and deal damage even if Sivir dies while it is traveling. This includes both the damage on the way out towards the target as well as the damage on the way back.

You can see this happen in this video:

(Note that the post-death damage is dealt to the CREEPS, not to LeBlanc)

For historical records, here are the relevant frames from that video: Boomerang on its way out, while alive

If you focus your attention on the circled creep, you can see that in the second frame it takes damage from the Boomerang Blade after Sivir has died.

Boomerang returning after death