One thing worth noting before everything: These characters are all familiar with different versions of each other, they don't know anything about each other, but their experiences with their own versions would not be erased. I'll bring this later, but let's start.
In terms of AP vs Dura, Lady has a 3.6 advantage with Kalina Ann's big missile while Dante has a <3.17x AP advantage, they are likely either even or Dante has a small edge in that regard. Since this is DMC 3 Lady, a lot of her things are unusable, nerfed, or just not there. She doesn't have the shotgun, the multiple grenades of her "DT" in DMC4, just the ones she has in DMC3. Kalina Ann is also not as great, it doesn't have its homing capabilities on it's main missile and Hysteric seems to have a lesser degree of homing when compared to the Kalina Ann she used later on her life.
Lady's best skill feats are also arguably not here, it being her disarming Trish and her firing skills in DMC4, it is still pretty great and has great showings on DMC 3, such as on
Mission 6, Mission 9's
beginning cutscene and
ending cutscene, but one thing to note is how it seems hard for her to
shoot targets while moving, which is a problem since Dante doesn't stop moving when fighting, as shown in the first episode where
Dante faced a few demons in episode 1, when
he faced the
mercenaries in
episode 2, when he faced
Agni and Rudra, in his fight with
Cavaliere and the other demons (The fight is too big so this video has some cuts) and
when he faced
Mutated Rabbit so hitting him is a problem.
That is also combined with the fact Dante and his own Lady (Who he should scales to in relation to hand guns) are very adept at hitting small targets
while moving (As shown
when he shoots a demon while moving and when said demon is holding a hostage in his face,
when he shoots a lightbulb without even looking at it,
when he shoots Lady's foot gear while trying not to hit her,
when he shoots a small pipe while wall-running,
when Lady shoots a small target from very far away with a single bullet and
when Lady hits two small moving target while driving a car with a single bullet for each), so shooting Game Lady's guns or even Kalina Ann's small missiles shouldn't be hard. In CQC, Dante should have the advantage, his LS is miles better then hers, and she doesn't have impressive Martial Arts showing. On the top of advantages, Dante is also a better acrobat then her, which means gaining distance from him is very unlikely.
I doubt Dante would try to kill Lady, it's not his thing and Lady is someone he knows and likely has an affection towards. Lady, meanwhile, knows that her Dante can survive headshots, and she constantly goes for them, which would incap Dante. The thing is, once again, it'll be very hard for her to shoot him since he keeps moving. There is also the fact Dante would expect certain things from Lady, Netflix Lady uses several gadgets and used subterfurge to take him down, he would be wary of those and would try to avoid her shots as much as possible, since he would believe those are the Anti Demon Bullets, it wouldn't take long to notice she is going for his head, which is more of a reason for him to avoid it or deflect it with the Rebellion (Something he is very good at).
Kalina Ann can easily be dodged due to lacking the homing capabilities and the Hysteric shouldn't be nearly as strong as Kalina Ann's main form of attack. In CQC, Dante can probably take away her guns (If he doesn't do it from ranged since he hit more smaller targets) just like he did with the Mercenaries back in episode 2, Lady has little hope of actually winning on him from that distance, Dante is much more skilled and his LS is way higher then hers.
Dante would eventually wear her down in CQC to take the win, once again, he wouldn't kill her, but she doesn't have regen to shrug off any hits in the head, and she lacks any actuall means to hurt Dante without her weapons, so I'm voting Dante
Edit: Put examples of Both Dante and Lady's gun feats
Edit2: Put more examples of how Dante fights
