Riho's passive reflect can (and probably should) trigger Lydia's A1 passive and Deterrence. The issue comes in where the responding attack doesn't trigger until after Riho's skill is chosen on her turn.

For example:

T1: Lyssandra uses A3 - Riho is frozen and reflects it. This triggers Lydia's A1, but Lydia doesn't use it.

T2: Riho is boosted from Lyssandra and takes the second turn. Select A3, Lydia immediately interrupts, A1's Riho and fears her, turn is lost. 

Alternatively Deterrence triggers from an nuker and kills Riho after you've already started Riho's turn and chosen a skill.

Additionally with the Lydia interaction. It seems that because Riho isn't feared after her turn starts, the fear duration doesn't decrement at the end of her turn. Which means she can (and in my case has) lost two turns to a single turn fear in addition to not knowing that she was feared at the start of her turn.