[SolemnGolem]

The biggest problem I can see is that the Angelic Emissary is fast. It has a flying speed of 38, so in one turn it could put itself at a distance where normal spell attacks have difficulty hitting due to the range modifier.

I was flipping through the Magic sourcebook and it seems that the lich could try crippling a wing of the Emissary. Although the Angel doesn't have blood, vitals, etc. it still has (Winged) as a limitation of its Flight power. Presumably, a suitably damaging spell might work, as the wing has HP/3, but the big challenge would be launching the spell quickly before the Emissary flies off into the distance.

The big benefit of outright damage is that (if it hits) the Angel doesn't get a Resistance roll, which is important because of its MR bonus.

Pyramid 3-48 p.5 has the spell Assassin's Blessing, which gives +3 to rolls in an attempt to kill (well, "assassinate") a given target.

Pyramid 3-28 p.20 has a simplification of Ceremonial Magic which could allow a mage to rack up bonuses in casting a spell through expenditure of prep time, along with bonuses for materials, sympathy, contagion, and knowledge of its true name (and maybe a bonus for sacrificing a bishop of the Angel's flock if the Lich is feeling sanguine).

In Power Ups 1: Imbuements, p.9 has an imbuement called Homing Weapon, which allows a weapon to ignore range attacks as long as its 1/2 range is fast enough to catch up to the enemy. Lightning Bolt's 1/2 range is 50, which exceeds the Angel's flight of 38. (p.11 covers the mechanics of giving imbuements to spells). Further treatment of this is covered in Pyramid 3-36 p.25 generally covering caster power ups and imbuements for spells.

Pyramid 3-13 p.39 has a Spell Bottle, in which the Lich could store lightning (in a bottle!) and then attack the Angel with it, although the idea of hitting a wing would be tricky.

Somebody once also recommended a Pentagram, but I have done limited reading on that and I'm not sure how the Lich could "chase" the Angel with one :(