Is tri force still good on lucian?

Definitely. I doubt it's still worth rushing over IE, but it should be a 2nd or 3rd build item. That passive is OP.

It's viable. Not the strongest build, but everyone has preferences.

When it comes to damage, PD/SS are supposedly better.

Otherwise, you need to consider the utility behind Tri-Force, as the health, mana, AP, and huge MS bonuses are things not available through other build options.

Usually people build tri force first because

1. They couldn't afford a full BF sword and was just a few hundred short.
2. Said player is in a lane where they die from a burst and need health from Phage
3. IE is unnecessary due to the fact that you need move speed from phage and zeal