Arwen, Mortal Queen

Arwen, Mortal Queen enters with an indestructible counter on it.
{1}, Remove an indestructible counter from Arwen: Another target creature gains indestructible until end of turn. Put a +1/+1 counter and a lifelink counter on that creature and a +1/+1 counter and a lifelink counter on Arwen.

The Lord of the Rings: Tales of Middle-earth

Arwen, Mortal Queen enters the battlefield with an indestructible counter on it.
{1}, Remove an indestructible counter from Arwen: Another target creature gains indestructible until end of turn. Put a +1/+1 counter and a lifelink counter on that creature and a +1/+1 counter and a lifelink counter on Arwen.

If the target of Arwen's second ability is illegal as it tries to resolve, the ability does nothing. You won't get to put any counters on Arwen.

You remove the indestructible counter from Arwen as a cost to activate its second ability. If Arwen already received 2 damage earlier in the turn, it will be destroyed due to having lethal damage before you get to put a +1/+1 counter on it.