How do we troubleshoot and fix things on our 2003 Lexus GS300

Ok, here's what I'm seeing. You first need to fix the misfiring cylinder number four. When a cylinder misfires the unburned gasoline goes into the exhaust system, where the catalytic converter is. The catalytic converter tries to eliminate the excess gasoline to keep tailpipe emissions where they need to be. In doing so the catalytic converter is overheated and fails. So what has happened is the engine misfiring has ruined the catalytic converter. Now for the EVAP system. A small leak needs to be diagnosed with a smoke test. Smoke is forced into the gas tank, which is part of the EVAP system, and the mechanic carefully inspects the EVAP system lines. Where smoke is seen coming from the EVAP lines there's a leak that needs to be repaired. The incorrect purge flow is most likely a bad purge valve. The purge valve regulates the amount of gasoline fumes flowing from the gas tank, through the EVAP system lines, and into the engine to be burned. Do NOT waste your time and money on replacing the gas cap. The gas cap will be pressure tested as part of the smoke test. So, in this order, fix the misfiring, fix the EVAP system, and last replace the catalytic converter. There are RARE instances where the downstream oxygen sensor is responsible for a false catalytic converter code, but again, don't waste your time and money on a new oxygen sensor until it's been properly diagnosed. Personally I've never had a bad oxygen sensor throw a catalytic converter code. But it does happen, RARELY. Hope that helps! Jim