Lukka, Bound to Ruin

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.