Don't understand. If you are willing to take an evening flight to LAX and spend the night there, you can just use multi-city search to get this on one PNR. With the overnight layover, there's no way to get this to fare out on a single fare, it's going to have to be multiple fares. If you are willing to fly Basic Economy, you will have to book as separate tickets because you can't combine Basic Economy fares on a single ticket unless it is a roundtrip routing. LAS has a potential alternative option as there is an early AM UA flight on LAS-LAX and UA/AA concourses are connected behind security at LAX. There's obviously some risk there as you would be on separate tickets and would not be protected if something happens with UA flight.