The lowest base movement speed in the game is 325. At this speed, Lich Bane grants 16.25 movement speed.
The movement speed stat only increases flat movement speed, and will not interact with other percentage increases.
Lich Bane's passive is considered an on-hit effect and, as such, is capable of being applied to skills such as Ezreal'sMystic Shot and Gangplank'sParrrley, which effectively adds a 50% AP ratio to those abilities in addition to their natural AD/AP ratios.
Lich Bane scales with ability power while Trinity Force scales with base attack damage. For some hybrid champions, it may be better to buy Lich Bane because once the champion reaches level 18, it becomes impossible to increase the damage from Trinity Force with items compared to Lich Bane. The proc from Lich Bane far surpasses Trinity Force with a Rabadon's Deathcap alone on the majority of champions, not to mention other AP items.
The highest Trinity Force is of 260, achieved by Cho'Gath and Skarner at level 18. Lich Bane beats it out even on those champions at 281 ability power.
Lich Bane does not proc spell vamp nor lifesteal.
Lich Bane is especially deadly if combined with an AA modifier, such as Mordekaiser'sMace of Spades or Twisted Fate'sPick A Card massively increasing the AP ratio on the ability, and is even more effective if the user can force the use only minding the 2 second cooldown.
Similar to Trinity Force, Lich Bane synergizes well with cooldown reduction, enabling champions to proc the bonus damage as often as possible while minding the 2 second cooldown; the 10 second bonus damage buff does not stack. Using two skills in quick succession will not accrue two stacks of bonus damage, but one.
The effect by Lich Bane can be seen on the champion as a purple glow. For example, Kog'Maw will have a glowing mouth, Shaco will have glowing hands, and Master Yi will have a glowing sword, etc. The glow only appears after using an ability.
The same thing will occur with Sheen, Iceborn Gauntlet and Trinity Force. You can easily distinguish between Lich Bane buff and that of the other items by looking at the color.