If you are still lying to your SO - as you noticed yourself, white lies are still lies - you are still actively addicted. Once I had discovered my boyfriend's addiction, I thought that once he knew that I knew and that he had my support and understanding, there was no more reason for him to lie to me. But I was so wrong. Whenever I came into the bathroom or study room and he was suspiciously staring at the home/lock screen of his phone/desktop of his PC and I asked what he was doing, he still kept lying to my face, every time. And even though my intuition told me something was wrong, I refused to believe that he would still continue to lie to me. One year after dday and finding hard evidence that he had still been looking at porn behind my back while pretending to have quit, I left him (temporarily). Knowing that he had lied to me was infinitely worse than being told that he had looked up some sexy pictures for a few minutes. And he also would argue that he was just 'protecting' me from feeling hurt. That is addict-logic. There is no way you can justify lying to your SO. There is no way you can justify deception of the person you love. You are just escaping the responsibility and consequences of your own actions. Because you don't know how to handle the feelings of having hurt your SO. You haven't learned how to deal with the guilt/shame of having disappointed her and her response to your actions reminding you of your mistake. You have learned to avoid dealing with these feelings in a healthy way by becoming addicted to porn. You need to relearn how to deal with feelings of having done something wrong (guilt =/= shame), without escaping them and not admitting them to yourself, lying to yourself and to your SO in the process.
This was and still is a problem in my relationship. Me resenting my boyfriend's actions (=him looking at porn, violating my boundaries) is perceived as me resenting him as a person and feels like an attack on his self worth and value as a person/boyfriend. It triggers feelings of shame. It triggers his fear of being rejected because of not feeling adequate enough as a person/boyfriend. And the only way he knew how to deal with those feelings was to escape them with porn. He has to learn to face them head-on, without him being lead to believe that his whole self is flawed or bad because of a bad/wrong action. Everyone is allowed to make mistakes, it's only human. Especially with an addiction, one is not fully in control of their actions. A bad action doesn't make anyone a bad person or a failure. A healthy way to deal with a mistake is to acknowledge the mistake, take responsibility for it and learn from it. You can never change something and grow as a person if you never admit a flaw in your behavior/actions. Some people just haven't learned that, because of traumatic events in their childhood/adolescence, adopting unhealthy coping mechanisms. My boyfriend for example was bullied in school, which I believe is the root cause for his unhealthy coping mechanisms.
I don't know if any of this applies to you, I don't know how you define a 'white lie'. But as soon as your wife asks you something and you know you are intentionally hiding something from her that you feel like she wants and needs to know, you are deceiving her and betraying her trust. You are not truly in recovery then. Just my opinion.