Except that's the real Lady Deathstrike on this page you posted, not some cheap copycats.
Lady Deathstrike HAS an Healing factor, every X-man knows that and that includes Kitty Pryde. That she would go hardcore on her as a result makes much more sense than her going hardcore on sapien soldiers (who'll probably lose their legs following their confrontation with her) or on crude fac-similes whom she had no clue if they were able to sustain the same kind of damage than the real Lady Deathstrike without dying.
I know it's Always complicated with you to highlight NUANCE in this kind of discussion, but please, do try and perceive it here, because of how obvious said nuance is.