The issue with making such a thing "useful" is that Trinity Force costs 4060 gold while Lich Bane costs 3460. Assuming you've also built a pair of boots, that's roughly 8500 to 9000 gold spent on items, which means you're quite a bit into the game, making the build useless as you'd hardly get any +damage out of Lich Bane due to lack of Ability Power items (110 between it and the trinity force) and you'd be extremely squishy.
You're better off getting a Black Cleaver or something to sync with the Trinity Force. It'll add about the same amount of damage that the Lich Bane would due to activating an ability, but you'd also have the added bonus of shredding enemy armor. Alternatively, something with high crit damage would be nice so that your attacks after activating an ability have the chance to inflict extreme damage.