I would suggest that maybe Luke wasn't going all-out but he was in a legitimately murderous mood.
Wow, really? Holding back in murderous mood?
Luke tried to cut off his own nephew's head at first possible opportunity for torturing his son. Why on earth he would hold back on a non-relative that killed his wife and who he wholeheartedly intended to kill? How does it make sence at all???
The only possibility is that the lightwhip makes it harder to blitz because of the length and unpredictable nature of the attack pattern. He didn't have the shoto as well.However, after looking at the fight, Lumiya does actually block his attacks with her lightwhip handle. Multiple times, its implied.
So blocking with hilt means she wasn't fast enough? Lightwhip is soft by the way, hilt is the only thing that can be used for actual blocking.
This "hold back" thing gets old, if Luke holds back, it doesn't mean that he holds back on speed.
This:
"That's enough." Luke advanced, activating his own lightsaber. Valin raised his in a preliminary block. Luke struck, twitching his blade out of the most obvious line of attack, and the blade sheared the hilt of Valin's weapon in two, not harming him.
Valin's blade switched off as the weapon's lower half dropped into the darkened urban chasm below. Valin took a step back, the last step he could afford before dropping off the front of the speeder, but Luke's advance was near instantaneous. The Grand Master slammed the butt of his own weapon into Valin's temple.
Luke held back on Valin, yet, took full advantage of his superior speed to incapacitate him without any harm.
Luke had his shoto in first fight with Lumiya, yet, couldn't do a thing to her because he didn't have significant speed advantage.
Moreover, Lumiya is not the only example, where Luke's speed can be compared. We have fight with Nyax.
Let me remind of his feats.
1. His strength was so enormous that single strike could knock Yuuzhan Vong over and drive Luke back.
2. His speed was such that he dodged Voxin and cut him in two with single slash. In comparison for Anakin's strike team killing Voxin was a "routine work" and they acted in combined effort.
3. Apart from super strength and super speed he, also, was equiped with 8 lightsabers.
Yet, Mara and Tahiri performed as good as Luke against him. The only thing that makes Luke stand out is that he managed to kick Nyax ones throughout entire fight.
I am willing to concede that Bane might be as fast as Sidious or Luke, despite the fact that he is less powerful. After all it's normal for less powerful characters to match speed of superior ones:
Dooku/Yoda, Dooku/Anakin, Sidious/Windu, Mara/Jacen and the most obvious ones Luke/Abeloth and Kenobi/Anakin.
But it is unreasonable to assume that Bane's speed is superior to everyone because of a non-combat feat that comes from an author in who's book average lightning turns into ash instantly.