The best replacement for life on hit is life per second.

The best alternatives to life on hit are rated as following:
★★★★★  life per second
★★★★★  life leech
★★★★★  vitality
★★★★  lifesteal
★★★★  area damage
★★★  lifesteal monk
★★  life regen
★★  lifesteal barbarian
★★  life on kill
★★  lifesteal ww barb
★★  lifesteal wizard
★  life regeneration
★  life per spirit spent
★  lifesteal demon hunter
★  lifesteal diablo 3
★  lifesteal witch doctor
  life steal
  life leach

Your alternative for life on hit is not listed? Suggest!
Speaking about life on hit, one probably shouldn't forget about archon.

Other search terms related to life on hit and their ratings are:
★★★★★ archon
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life on hit
life per second
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