Lukka, Bound to Ruin

• WOTC Official Reminder Textofficial rules
  Compleated — Phyrexian mana can be paid with 2 life. If life was paid, this planeswalker enters with 2 fewer loyalty counters.

• WWizards of the Coast2023-02-04
  Official Ruling
  Other replacement effects that would change the number of loyalty counters Lukka enters with will apply as normal.
• WWizards of the Coast2023-02-04
  Official Ruling
  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.
• WWizards of the Coast2023-02-04
  Official Ruling
  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.
• WWizards of the Coast2023-02-04
  Official Ruling
  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.
• WWizards of the Coast2023-02-04
  Official Ruling
  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.
• WWizards of the Coast2023-02-04
  Official Ruling
  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.

Rulings via Scryfall