When Kayn has Doran's Shield (Tank) and moves for the 2nd time in a turn, does Tank still apply to him?

Ruling: No, Tank does not apply to Kayn when he has moved twice in a turn. Kayn is exempt from mandatory assignment considerations, which includes Tank.

Nuances:

• While Kayn is exempt from mandatory assignment (including Tank and lethal damage requirements), you can still choose to assign damage to him if desired, though it won't be dealt to him due to his immunity.
• No amount of damage assigned to Kayn can be considered "lethal" when he has moved twice.
• The exemption means you are not required to assign damage to him, but you are not prohibited from doing so either.