When one of my units becomes mighty and I end my turn, but forgot to use Fiora Grand Duelist legend card for its effect, may I do it in the next turn for that unit that became mighty in the previous turn?

No, you cannot use Fiora, Grand Duelist's ability on your next turn for a unit that became Mighty on a previous turn.

According to the card's ability, it triggers specifically "When one of your units becomes [Mighty]." This is a triggered ability that must be resolved at the moment the condition is met (when the unit's Might changes from less than 5 to 5 or greater).

Because the trigger condition occurred on your previous turn, the window to use the ability has passed. You cannot retroactively apply the trigger on a subsequent turn.