Lo Sasuru Acharei Eineichem is a Lo Sa'aseh on Hirhur Halev. How could there be a Lo Sa'aseh if Chazal say that a negative Machshava H' doesn't consider a Ma'aseh Aveira? R' Chaim Vital explains that a Chet is a combination of 4 things - Thought in the Brain, thought in the Heart, Speech, and Action. So thought can be in the brain or in the heart. A thought can pass throught he brain and never make it to the heart. For that there's no Lo Sa'aseh, H' does not consider that a Ma'aseh Aveira. The Aveirah is only if the thought goes to the heart.
Now, how could we be commanded to control the thoughts of our heart? Can we control them? Yes, we can - with Torah. Avos D'Rebbi Nosson (20) says, if one puts the words of Torah on their heart it gets rid of the thoughts of Aveira. Barasi Y"H, Barasi Torah Tavlin (Kidushin 30b) - by saturating our mind with Torah, thoughts of Aveira will dissolve. The Rebbe of Kuvrin learns this from the Ramah at the beginning of Shulchan Aruch that says when one takes to heart the fact that HKB"H, Whose existence fills the world, is standing over him, watching every action, he will instantly achieve Yirah - fear of heaven. But haven't many tried without success? If it remains only a thought it won't have any effect. It has to penetrate the heart. This also effects the thoughts in the heart - if you allow the thought of H's constant watch over you to enter your heart those thoughts will disappear.
Another Avos D'Rebbi Nosson (24) says that Torah gets absorbed in the blood - that's how you become a Metzius of Torah. In that way the Torah is Tavlin against the Y"H, by entering the HEART.
Torah taken to heart creates a spiritual light that shines within a person. Tzitzis has a similar effect, but on the body. Tzitzis creates a protective light around a person's body and even effects their thoughts. The Bracha on the Talis (the Arizal would make this Bracha on Tzitzis too) is "Lhisatef BaTzitzis", because the effect of Tzitzis is Misatef - it completely surrounds the body. This is why the Seforim say it's an Inyan to wear Tzitzis at night too - not to break this protection. The Mitzvah of Tzitzis corresponds to a fulfillment of all Mitzvos because its effect is all encompassing, on all parts of the body. The famous story of the man who was meticulous with Tzitzis who was saved from Aveirah in Menachos 44a supports this idea.
In these 2 ways we are protected from the thoughts of the heart, and avoiding this Lo Sa'seh is within our reach if we allow Hashem's Torah and the special Mitzvah of Tzitzis to enter our heart, our bloodstream, and completely envelop us. To the degree that we do this we will be protected - that's Hashem's promise.
[The question I have had, and that many others have had, is how can I have impure thoughts if I learn Torah, if I know that H' is always watching? What happened to the special power of Torah to protect us from this? "Hamaor Shebah Machziro L'Mutav." Has all my Torah learning helped? Why am I still spinning with impure thoughts and actions?
The answer is that Torah does have a special power to keep us pure, but not if it only remains in the mental state, as a thought in our mind. For Torah to protect us it must enter the heart, it must make an emotional connection. I think that's why Chazal compare Torah to a Tavlin - a medical remedy. Medicine has an effect when it enters our bloodstream - when the heart pumps it throughout the entire body. If it remains localized it has little effect. If we connect with Torah emotionally, not just as a mental activity, then the medicinal powers of Torah will rid us of all impurities in thought, and consequently in action. ]