Despite riot claiming to want consistency and clarity they can be really inconsistent.
Lux passive counts as a separate instances of damage despite only needing one action to perform (see FQC), this total's 3 instances of damage and procs TLD.
Sona Q / powerchord also counts as 2 different instance of damage (see FQC) with the Q projectile that should equal 3 but the combo somehow counts as only two for TLD.
Likewise sona Q does not affect turrets despite being a consumable AA empowerment rather than a passive/ on hit effect.
Thing like oriana's clockwork, nashors and ardent censor don't work on turrets since they are passive on hit effects i.e. you can get multiple procs off (during a certain window). lichbane, sheen and diana passive do work on turrets since they empowers next auto after which the buff is consumed.
Sona Q clearly fit's the latter but somehow counts as the former for turrets.
My only guess is that riot is actively trying to keep sona away from proplay. Why? this would make sona pretty strong with laneswap / turret trade situations we see in the LCS since it would significantly increase the speed at which they are taken.