If you are looking to book flights on one itinerary (PNR), the reservation systems will not book a connection less than the MCT (minimum connecting time). I suspect that the MCT at LAX from Int'l to domestic is more that 1 hour 5 minutes.
If you are booking separate itineraries, then you are free to book them as you like. However, if the incoming flight is late, you are pretty much on your own if you miss the connection as the airlines are not required to re-accommodate you.