Personally I would love Riot to revisit Fiora and give her some love, she's really fun and I would love to see her fit in somewhere.
Duelist - Compared to other sustain passives is very lackluster. At level 18 you get 100 Health over 6 seconds, assuming you hit just champions 4 times. I think if the passive was over a shorter period of time or higher base health back or a combination of both it would be better and would encourage trading and actually dueling.
Lunge - Once Fiora reaches her target she needs to auto attack that target, much like they did for Akali's Shadow Dance.
Riposte - Needs to be changed the Physical Daamge and scale off AD. Concept wise, she's a Duelist that slices up her enemies with her sword, why does she deal Magic Damage when parrying? I think this would also make it more rewarding for using Riposte during duels.
Burst of Speed - This skill is fine, but I think it would nice if it lasted a little longer to ensure she can get kills. I feel like this is Fiora's bread and butter skills because she is an Auto Attack based champion.
Blade Waltz - The skill is great but... There are many situations where you get "carried away" by champions, ie using Blade Waltz on Shyvana as she Dragon's Descent. Where I don't find it too much of a problem, I think it would be interesting if she was able to Silence her initial target. Also removing the channel time on the cast would be great.
The main thing Fiora doesn't have compared to other Melee Carries is she has no CC of any kind. This makes her not viable in Top Lane as most of them have a combination of CC, durability, self buffs, good damage, and sustain. Where Fiora has no CC, no durability, a good self buff (Burst of Speed), mediocre damage even with Blade Waltz, and mediocre sustain.
Well this ended up being a longer response than intended, my bad.