Oh, come on. You did so well with the first two.
Slaanesh isn't just about lust, but craving in all forms.
Greed, gluttony and pride are as much Slaaneshi sins as lust, and obsession is its hallmark: look at Noise Marines. It'd be quite easy to have a Sister who, sick of the strict military rations, bread and water, starts gorging on exotic, rich food in secret. Eventually, her desire for new tastes overwhelms her, and she secretly begins devouring the flesh of her enemies.
It's not too far a stretch from there before she falls straight int 'Nesh's arms.
Tzeentch would also be more scheming than xenotechnical, plotting how she can bring more hope to the people she protects- until she loses sight of actually saving the people, seeking only to make them hope (something that can't happen unless they're in peril), and subverts her own protecting innocents by deliberately drawing in enemies to fight.