Keeper of Fables's ability triggers even if it's dealt lethal damage at the same time that non-Humans you control deal combat damage to a player.

If non-Human creatures you control deal combat damage to two or more players at the same time, Keeper of Fables's ability triggers for each of those players.

Because creatures with first strike deal combat damage before creatures without first strike, Keeper of Fables's ability can trigger twice during one combat if your creatures deal combat damage to one player at different times.