While waiting for actual damage calculation, I got super excited about Lila's global buffs and played around with FFBE equip. Here are some of the preliminary stats and findings:

Non-stmr build for Lila: Link. Build score when T-cast Heaven Shift: 1888936

Stmr build for Lila: Link. Build score when T-cast Heaven Shift: 2694869

For comparison

Non-stmr build for Hyoh: Link. Build score when T-cast Servant Blade: 2729101

Stmr build for Hyoh: Link. Build score when T-cast Servant Blade: 3694080

It seems even with buffs, Lila still falls behind. But hey, that does not stop me from using her to clear trials. At least, she is better than her counterparts in JP. I welcome that.