Lean codes and P0420 can all be caused by misfires from burned open plugs thanks to the wasted spark ignition. When a cylinder doesn't fire there is unburned fuel and excess oxygen in the exhaust - but O2 sensors measure oxygen.
The P0420 code can be tricky - it is looking at the upstream and downstream O2 sensors to try to figure out how much the cat is doing. It is expecting the downstream O2 sensor to show a different signal from the upstream O2 sensor. Unburned fuel and excess oxygen from misfires can mess that up - there was already excess oxygen upstream, and then the unburned fuel goes into the hot cat. It may not com out cleaner so the system thinks the cat is bad.
The wasted spark system has 3 coils, and each must fire the spark across one plug on each bank every time. Because one plug is firing "backwards" it removes material from the center electrode and the gap grows rapidly. Since the coil must fire across both gaps to make a spark, if it misfires it may do so on both banks. Also, as the gap grows the voltage required to arc grows, and if the wires are marginal the higher voltage may cause the wire to break down before firing a spark on the plugs.