If a creature is indestructible, will it die if an appropriate amount of -1/-1 counters are put on it?

If a card that is indestructible has toughness that reaches 0 or less due to any effect other than lethal damage it will be set to the graveyard. If you are able to put a counter on or use a spell with gives the Ornithopter a */-2 or more the Ornithopter would immediately be set to the graveyard. However a spell light Lightning Bolt would not kill the Ornithopter as that would be lethal damage in that case.