What do you mean by programming?
Are you referring to something along the lines of this:
Tears of a Machine: The Humanity of Luv in "Blade Runner 2049" | Features | Roger Ebert
Personally I disagree with the premise. I never got the sense that she was an unwilling participant in Wallace's plan.
Her operating principle was to be the best of all of the replicants and prove herself to her "father".
The two examples cited in the article, I actually see differently.
1. When she cries during the stabbing of the newly born replicant.
Another interpretation of that scene could be that she sees in the murdered replicant a reminder that she herself, is unable to have children, and therefore not living up to Wallace's standard for replicant perfection.
Or a realization that she too is replaceable if she fails to assert her position as the best of the replicants.
It's a plausible view of the character given how often she tries to measure herself against others.
2. She cries upon hearing the knowledge that the child is dead.
“In the face of the fabulous new, your only thought is to kill it ... out of fear of great change."
The author believes that she internally hopes for some form of future for her species.
"It isn’t until later that Luv realizes this news may not be the truth. However, this miracle child, if found, would symbolize hope and change and love to all synthetic life."
Personally, I think it has more to do with the failure in her mission and the failure of Wallace's plan. She ties her own worth and well-being to meeting his needs. Her job was to bring the child to Wallace in order to enact his plan for conquering the stars. The death of the child potentially ends that dream and her role in it.
Humans, particularly children, can be motivated similarly without any need for technological "programming". Behavioural programming sure, but that's irrespective of whether she's a replicant or not.
I am sympathetic to Luv, certainly, but that never extended to where I think she ever second-guessed her actions or took issue with anything that Wallace was undertaking.
The Rachel clone was executed by Luv without any restraint or regret that I could distinguish. Rachel failed in her purpose and had no further utility.
With respect to non-replicants, they also hardly warranted notice. Luv took actual glee in destroying Joi and executing Madam, and barely registered the death of the forensic scientist.
Her psychopathy appeared to be linked to her overwhelming desire to assert her superiority and worth to everyone, but particularly to Wallace.
"I'm the best one."
Again, just my thoughts and interpretations of the film. I am sure there are many.