Other replacement effects that would change the number of loyalty counters Lukka enters with will apply as normal.

If some of the targets of the last ability become illegal, the original division of damage still applies, but the damage that would have been dealt to illegal targets isn't dealt at all.

A hybrid Phyrexian mana symbol contributes 1 toward the mana value of a card, even if life is paid for it. Specifically, Lukka's mana value is always 5.

You can't choose more targets than the greatest power among creatures you control as you activate the ability, and each chosen target must receive at least 1 damage.

The compleated ability looks only at whether a player chose to pay 2 life for a Phyrexian mana symbol as they were casting the spell. If a player paid life for some other reason while casting the spell, that will not reduce the number of loyalty counters the planeswalker enters the battlefield with.

For Lukka's last ability, you announce the targets and how damage is divided as you activate the ability. Once the ability has been activated, the greatest power among creatures you control no longer matters for this ability. This means once you announce you're activating it, no player can respond to try and lower that power and decrease the damage Lukka can deal.