The best replacement for lich bane is trinity force.

The best alternatives to lich bane are rated as following:
★★★★★  trinity force
★★★★  iceborn gauntlet
★★  nashor's tooth
★  trinity force poppy
★  trinity force akali

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Speaking about lich bane, one probably shouldn't forget about trinity force.

Other search terms related to lich bane and their ratings are:
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lich bane
trinity force
iceborn gauntlet