No, you cannot activate the ability after lethal damage has been dealt. You can, however, activate the ability before the damage has been dealt.
In a normal situation, you would lose the game as soon your life total is 0 or less. Losing the game is a state-based action, so no-one receives priority before losing. The game ends immediately (presuming two player game).
However there are cards that prevent you from losing the game while having 0 or less life. In this case, activating the ability of Angel of Grace will cause you to gain life so that your life total becomes 10, even after "lethal" damage has been dealt.