You may remove any +1/+1 counter from Deathbringer Thoctar to activate its second ability, not just a +1/+1 counter put on it with its first ability.

If Deathbringer Thoctar and another creature are dealt lethal damage at the same time, Deathbringer Thoctar will be put into a graveyard before it would receive any counters. Its ability will still trigger, but it will do nothing when it resolves.