Steve Butram wrote: It appears that the wire was undersized for the intended load or the wire was loose on the terminal. We saw a lot of this when Aluminum wire was used. Check the wire size and breaker to see if they are compatible.
Steve has it nailed. You were using a 15 amp outlet. If that is an original outlet then the wire is probably 14 awg. For outside you should have 20 amp GFCI outlets at the beginning of each run using 12 awg. You can use 15 amp but have to be careful what you plug in.
I don't know how many amps your lights draw but I would make sure your wiring matches your draw. You say you split the circuits, but are you sure you are on a different circuit or is it just another outlet that is on the same circuit? If it is the same circuit the load will shift to the breaker or light switch and possibly cause similar problems only now they will be inside your house.
If you didn't replace the outlet with a gfci, I highly recommend it. If your wiring is 14 awg then get a 15 amp gfci.