Can someone explain me how the NEW btrk buff work?

the on hit passive now applies lifesteal

Previously, you gained lifesteal when you hit, but only off the of the portion of damage coming directly from your auto attack.

So say you had 200 AD, and your target has 2000 hp, Old BotRK gives you (200 AD x 10% lifesteal) = 20 Hp back (not counting armor reduction)

New BotRK now gives you lifesteal on both portions of the damage. So (200 ad x .10) and (2000 hp x 8% hp damage = 160 damage x .10 lifesteal) = 36 hp back.

Also, if they had so little current HP that it would have done less than 3 damage, it did 3 damage instead. Now, if they have so little HP that it would have done less than 10 damage, it does 10 damage instead.