He’s got a head start on haki since Oda retconned tekkai as bootleg armament but this would have Lucci making similar leaps in strength as Lucci without the unlimited time to train, while working as a CP0 agent and seemingly without a teacher on Rayleigh’s quality. Which I don’t find realistic
CoA, CoO, CoC, base stats, skills, Gear4
There are levels to this haki training too, you not only need to learn coating but also strengthen this haki.
Luffy may have learned coating after a week or so considering ACoA and ACoC were achieved this fast.
Lucci is guaranteed to have the best trainers in the world, especially since they can teach fodder how to coat haki.
He might have had a year off before joining Cp0, we don't really know how much he spent training.
And doing some Cp0 missions while he's still training gives him even more chances to refine his skills, nothing wrong with that.