I’ve seen quite a few people using Moonblow rather than Glimmer on Lysithea (probably because it is her base kit).
So I’ve decided to do the maths.
The General rule is that the more foe has resistance, the better Moonblow get.
And at the opposite, the higher Lysithea’s attack is, the better Glimmer get.
I’ll use my own +1 Lysithea as test subject :
61 base attack (No Blessing / No Buff).
 (+ 8 from Death blow 4 A Slot.
 (+ 6 from Death blow SS.
 (+ 10 from Hades Omega.
85 base attack.
Lull Res will be calculated independently, as it reduces Moonblow aswell (i’ve tested it).
At first, let’s say Foe is a Red/Colorless foe
With 50 resistance :
 Glimmer damage : [85  (503)] x 1.5 = 57 damage
 Moonblow damage : [85  (503)] + [0.3 x (503)] = 52,1 damage
With 55 resistance :
 Glimmer damage : [85  (553)] x 1.5 = 49.5 damage
 Moonblow damage : [85  (553)] + [0.3 x (553) = 48.6 damage
With 60 resistance :
 Glimmer damage : [85  (603)] x 1.5 = 42 damage
 Moonblow damage : [85  (603)] + [0,3 x (603)] = 45,1 damage
Now, let’s say Foe is a Blue Foe
With 45 resistance :
 Glimmer damage : [(85x0.8)  (453)] x 1.5 = 39 damage
 Moonblow damage : [(85x0,8)  (453)] + [0,3 x (453)] = 38.6 damage
With 48 resistance :
 Glimmer damage : [(85x08)  (483)] x 1.5 = 34.5 damage
 Moonblow damage : [(85x0,8)  (483)] + [0,3 x (483)] = 36.5 damage
Now, let’s say Foe is a Green Foe
With 65 resistance :
 Glimmer damage : [(85x1.2)  (653)] x 1.5 = 60 damage
 Moonblow damage : [(85x1.2)  (653)] + [0,3 x (653)] = 58,6 damage
With 70 resistance :
 Glimmer damage : [(85x1.2)  (703)] x 1.5 = 52.5 damage
 Moonblow damage : [(85x1.2) (703)] + [0,3 x (703)] = 55,1 damage
Conclusion :
On Lysithea, because of her very high ATK, it takes HUGE amount of foe’s resistance for Moonblow to deal more than Glimmer.

Blue foes (weapon triangle disadvantage), is where Moonblow shines the most, but even then, 48 resistance is a very high amount most blue foe’s won’t have, and a 48 resistance blue foe (+Res ice mirror Fjorm / L!Julia) will destroy Lysithea on retaliation regardless of if she has Glimmer or Moonblow.

Red/Colorless foe, Glimmer is always better unless +10 F!Julia Asset Res with ATK/Res solo 4, or F!Julia with Sothis/Eir blessing, and even then, the difference is very small.

Green foes, Glimmer is always better in every situation.
Sidenotes :
 +ATK buffs on Lysithea / +ATK blessing on Lysithea /  Res debuff on foes, will tend to make Glimmer slightly stronger.
 +Res buffs on foes will not make any difference because of Lull Res
 ATK debuffs on Lysithea / + Res Blessing of foes will tend to make Moonblow slightly stronger.
You get the idea
Sidesnotes² (regardless of Lysithea) :
While Moonblow/Glimmer are great special because of their shortcooldown, they target a specific kind of foes (Moonblow aim to deal with bulky units, while Glimmer is great to oneshot squishys).
Others special that rely on your own character’s stat (Draconic Aura/Dragon Fang/Icerberg/Glacie/Bonfire/Ignis/Regnal Astra/Hero’s Blood) are much more consistent because they do a set amount of damage regardless of if your foe is bulky or squishy.
Therefore, they are my favorite in ARD.