Well, almost. I could be wrong but, if I remember correctly, the only information we have about the whole "keep me from my daughter" thing is where EC texted her friend that he was worried about that. Is that correct? So, we don't know exactly how it was stated. We only know how LE worded it in their affidavit and they are only going to lay out what they must to move the case forward. I'm thinking CL may have used that as his excuse, but not necessarily that he quoted NL as saying that. Cheaters (both men and women) say all sort of things that aren't true, to keep their shenanigans under wraps. As some WSers have pointed out, people with stars in their eyes will believe all sorts of crap their lovers dish out that everyone else can see through immediately and insist their guy/gal is different and would never lie like that.
If EC was unhappy with Jon and pushing CL for some sort of commitment, then "Honey, you know I'd rather be with you but, if my wife finds out I cheated on her, XXXXXX will happen and I'll never get to see my daughter" is a cheap and easy way to try and put a damper on any demands EC may have been making. It makes more sense to me that he never intended anything permanent with EC and was simply playing for time, until he could leave for Alaska and put EC in his rearview mirror. When that didn't work, he became desperate enough to kill her.
But, maybe I'm giving the piñata candy tosser too much credit.