League-of-legends – When is the cooldown on Lich Bane’s proc reset

As of today, 3 items give the most cooldown reduction, which is 20%:

• Nashor's Tooth

65 Ability Power, 50 Attack Speed, 10 Mana Regeneration. UNIQUE Passive: +20% Cooldown Reduction.

• Morellonomicon

  75 Ability Power, +20% Cooldown Reduction, 12 Mana Regeneration. UNIQUE Passive: Dealing magic damage to an enemy champion below 40% health inflicts Grievous Wounds on them for 4 seconds. (Grievous wounds reduces healing and regeneration rates by 50%)

• Frozen Heart

  90 Armor, +20% Cooldown Reduction, 400 Mana. UNIQUE Passive: Reduces the attack speed of nearby enemies by 20% (1000 range).

It is possible to have more than one Voidling out at one time, but even with 40% CDR, Malzahar can only have two Voidlings out. With absolute perfect play and ridiculous timing, you can actually squeeze out three. The first one will expire before the third is primed to be summoned, unless you have that aforementioned perfect play in which the first Voidling will expire a split second after the third is summoned.

Assuming you prime a Voidling (stack up three ability uses and wait for all your cooldowns), your next spell will summon a Voidling and you have three spells left. Since you need a fourth spell to summon a second Voidling, the second Voidling cannot be summoned for another 4.2 seconds (which is when Malefic Visions comes off cooldown, Malzahar's fastest spell). This is assuming absolutely no lag and concurrent spellcasting, which is impossible so we'll give it 6 seconds to account for targeting time and server response lag.

Which means your first Voidling will be out for 6 seconds when your second Voidling has been summoned. This means that you'll have 21 - 6 = 15 seconds of two-Voidling time. With judicious timing and luck, you can eek out a third Voidling, but this is extremely difficult and the benefit is very small as the first one will die just a hair of a second after the third is summoned, so there is very little difference in the total damage dealt.