You can just fight Wiz20 or Sorc20 with the help you get from Lich (I think, I don’t do Liches) and lose maybe 10% of your offense from EK while keeping your cool class progression from the interesting archetypes.
We probably have different standards for melee. When I say melee, for me it usually means:
- Power Attack with Mythic Feat, and it scales from BAB, +5 damage from each step for two handers
- Cleaving Finish
- Improved Crit
- Outflank
- Shatter Defenses Line
- spend 95% of his combat time hitting things with huge club
This kind of build is kinda pointless on Wiz20 or Sorc20, but fits well with EK.
I really wanted to do melee Lich for some time, just hadn't got to it yet, mainly because I've checked Lich special powers and really liked some of them meant for martials, like:
Fear Control
Lich gains a +4 profane bonus to attack and a +1 profane bonus per mythic rank to damage against frightened creatures, or ones under any mind-affecting effects. Additionally, all enemies within 10 feet of the Lich must make a Will saving throw (DC = 10 + double the mythic rank) or become shaken until the end of combat. A successful save gives immunity to this ability for 24 hours.
Weapon of Death
Lich can enchant items he wears with bane living and nullifying special abilities. If a creature is killed with the weapon of death, all creatures in a 15 feet radius suffer a penalty on caster level checks made to overcome spell resistance equal to twice the Lich's mythic rank until the end of combat.
4 level spell
Vampiric Blade
Your weapon becomes bloodthirsty. It deals (1d6 + caster level) additional damage, healing the wielder for the same amount.
From what I saw from the Lich spells, most of them, like Angel's, ignore SR and still hit for respectable damage even after successful save, so building a gish with max STR and medium INT/CHA is very attractive.