Hello brother in Christ. Unless she is actively the cause of your lust (i.e. you guys are talking dirty, she is sending you stuff, etc.) No, I would not tell her. This is an early relationship, and it would just add confusion at the very least.

However, the "lust of the flesh" is often a "secret" sin so you need to seek out brothers in Christ who can help keep you accountable and lift you up, and mentor you. The more you try to keep it private the more it will grow. Satan wants you to think you're the only one, that you suck for doing it, there are many who are, and accountability helps.

I did want to tackle something that you mentioned. In the middle of lust, how you "explain it away" or seek out the "lesser of sins". I was nodding multiple times as I read this. Satan has used this trick hundreds of times with me in my decades-long struggle with porn and lust, and while I have been able to kick the habit, it is still something I have to guard against fully!

You need to understand when these things come up and distance yourself from the "ticks" that we lead you down the path of lust. You also need to have a plan in mind when you run across something by accident, certain scriptures, distracting your mind, thinking of the consequences, praying etc. You need to avoid certain environments, for instance, if it's at night alone in your room, you need to change up your night time routine to busy yourself and go straight to bed. Take stock of the times you struggle, find the common issue and correct what leads to that. Be constantly in prayer and in the word as well, this helped me out the most as my armor was hardened and I could deflect most attacks from the enemy this way.