Trinity Force is only balanced because it deals damage 150% of base auto-attack damage. It would be far too powerful otherwise.

Lichebane is only "good", quite amazing really, because it converts ap to a damage modifier. Mages have lower average base damage on their auto-attacks than bruisers, assassins, tanks, etc and they are primarily ap focused. The only way to make Lichebane worth taking on a mage is to make it scale on ap, and this isn't a problem because that ap doesn't help their auto-attack damage for the rest of the time and they don't scale enough from spells or auto-attacks for the damage to be problematic.

Remember, Lichebane is designed for champions that otherwise have horrible auto-attacks, and it scales on a stat that is normally unrelated to auto-attacks. Trinity Force is designed for champions who get roughly 50% or more of their damage from their auto-attacks and would gain too much of an extra bonus if the item scaled based on an alterable stat.

think about an ezreal with 5 blood and a trinity in the way you think.
500+30+113= 660 with runes and masteries
660 + 115+660+6(of his q) = 1441
with shen procs on q = 1441+1441*1.5
lol 3602 damage on a long range poke