CL may have just told Erin that NL would keep his child from him, as an excuse to keep Erin from getting any ideas about a permanent attachment.
But I imagine that lots of wives, after an initial affair (CL and Erin), would have issued a few threats/conditions about what they would lose if it ever happened again. NL may have agreed to mend her marriage with CL the first time, but given him very explicit ideas about what would happen if he did it again. If so, his reaction as far as panicking about Erin's pregnancy and her alluding that the baby was his would be pretty extreme. Jmo but when it comes down to it, most men have every intention of staying with their wives, no matter how many affairs they have. Of course they don't all resort to murder if pressured, but it certainly is not the first time that infidelities have resulted in the death of one of the parties involved either.
I am thinking this guy CL is finally finished with his military career and ready to start his proper married life and a new career with family up in AK among his own family, maybe had been looking forward to it for years and then here comes Erin, from what was supposed to be casual fling to fill the hours, wanting him to throw all of it away and start fresh with her. No way he was going to do that, and no way was she going to even have the chance of interfering with his marriage on any real level.
Imo,the reasons people kill are generally selfish, to get money, to eliminate a threat to their desires, to cover up something they've done (extortion, i.e), to get drugs. Etc...CL fits right in with these types of motives.
All JMO.