Hardly anything about my patch is a secret. =P
I'll try and detail each of the Lucavi's themes to the best of my ability. Note that they all Cancel (or Absorb) Dark:
Cuchulainn- Specializes in Poison magic, using Bio. He halves Water and Earth elements, but is weak to Fire and Holy. In the DD rematch, he is flanked by King Malboros.
Belias- Specializes in Fire magic, and uses Oil in combination with his fire spells. He absorbs Fire, but is weak to Water.
Zalera- Specializes in death and status abilities, using Kill and Fallen One (think FFVI's version) to bring units to their deaths, however he is weak to Holy, which he casts. Note that you rebattle Algus during this fight as well.
Adrammelech- Uses a combination of Thunder magic, Berserk, and Stop to throw your party into disorder. He absorbs Thunder, and will eventually have Behemoth allies.
Hashmal- Uses a combination of Earth magic and Immobilize, as well as high-tier elemental magic. I forgot to make him weak to Wind in this version, but he will be in the next one. Absorbs Earth.
Ultima (1)- Uses Holy magic, Greater Barrier, and Logos to minimize your party's effectiveness.
Ultima (2)- Uses Ultima magic (obviously), as well as what she used in Vanilla.