Invoker Lillia
Items
Lillia with 2 Invoker is effectively a 45 mana unit since it will proc 1 time for 5 mana. Lillia with 4 Invoker is effectively a 30 mana unit since it procs 1 time for 20 mana per cast. You will usually play 4 invoker so Blue Buff is very good on 30 mana Lillia. Since Lillia’s traits do not give her as much AP as Fated or Arcanist, AP items are very good on her such as Rabadon's Deathcap and Archangel’s Staff. Other good items are Adaptive Helm, Nashor’s Tooth, Jeweled Gauntlet, Guardbreaker, and Red Buff.
Since this is a full AP comp, magic shred is important with Spark or Shiv. Antiheal is nice to have as with in every comp and Lillia is a great spreader with Morello, but oftentimes you may play Annie who offers a bit of antiheal.
Frontline items will typically be whatever components you have leftover; good frontline items include Crownguard, Warmog’s, Vow, Adaptive Helm, Dragon’s Claw, Stoneplate, Bramble Vest, Steadfast Heart, Evenshroud (if no LW), and Sunfire Cape (if no other antiheal). As always, pay attention to your item economy as Rods and Tears are very valuable so you should avoid building Crownguard and Vow unless you already have your carry items.
Positioning
Alune should be in the same row as your primary carry. Make sure you have your primary carry on the same side as your antiheal, magic shred, and strongest tank. Spread your backline to avoid enemy AoE, do not greed Umbral too much. Nautilus needs to be exactly in the middle, otherwise, he is very likely to only ult frontline.
Board Examples
Boards are just an example of what you might play at various stages. Upgraded units are often better than one star units that activate synergies, so make sure you look at your shops carefully for better options.
Stage 2 (Invoker not necessary for Kog)
Stage 3
Stage 4 (Level 8 without legendaries)
Stage 5 (level 8 with core legendaries)
Stage 6 (level 9 adding Udyr)
For an explanation of several alternate openers and item sets, check out Aesah’s Invoker Lillia video!