I had the same check engine light problem with the p0421 code. I could not pass emissions, so I took the car to the dealership, and they quoted me $1000. At the dealership they told me that catalytic converter was bad and needed to be replaced. I did some research, and replaced the rear catalytic converter. At this point I did not know that the 2002 Lancer has two catalytic converters. However, the check engine light came back on after about 50 miles of driving the car.
The rear catalytic converter for the 2002 Lancer looks as follows:
http://www.amazon.com/Walker-Exhaust-16185-Ultra-Converter/dp/B000VKXAW4/ref=au_pf_ss_5?ie=UTF8&Model=Lancer|307&n=15684181 &s=automotive&Make=Mitsubishi|72&Year=2002|2002&ca rId=001
The rear catalytic converter is located underneath the car, right in the middle. The downstream oxygen sensor is connected to the rear catalytic converter.
After the check engine light came back on, I decided to replace the upstream oxygen sensor. The upstream oxygen sensor that I bought was the following:
http://www.amazon.com/Bosch-15514-Oxygen-Sensor-Fitment/dp/B000VASNF8/ref=au_pf_ss_4?ie=UTF8&Model=Lancer|307&n=15684181 &s=automotive&Make=Mitsubishi|72&Year=2002|2002&ca rId=002
The upstream oxygen sensor is located close to the engine. When you open the hood, you'll see something that looks like a spark plug sticking out of the engine. Look for the heat shield (a piece of metal that has a picture of a crossed out hand). Use pbblaster or wd40 if the oxygen sensor is frozen in place. I had to use an oxygen sensor socket to remove the sensor. It was about $10, and it is definitely worth buying it. It sames a lot of time and effort.
I changed the upstream sensor because it was a lot easier to reach and replace than the downstream sensor. Plus, I had seen someone mention in the forums that the upstream sensor was a more probable culprit than the downstream sensor. I was also getting desperate and was willing to try anything that worked. The oxygen sensor did not fix the check engine light, even though it did seem to improve my gas efficiency a bit.
The last thing I attempted, which finally fixed the problem, was replacing the front catalytic converter. I took the car to autozone to get yet another reading of the check engine light. I explained everything that I had done to the autozone guy, and he said it was the front catalytic converter that was causing the check engine light problem.
The front catalytic converter is underneath the heat shield. It has four inputs which connect directly to the engine, and it has one output. The front catalytic converter is quite expensive. I found a few in autopartswarehouse.com, you'll find them under front catalytic converter or under exhaust manifold/catalytic converter. In the end, I bought the front catalytic converter from ebay because it was cheaper (about $350 including shipping and handling), and because there are sellers in ebay that sell entire replacement kits, rather than only selling the front catalytic converter by itself. The replacement kit included the front catalytic converter, all of the necessary bolts (even though you can reuse the old ones), the manifold gasket, and a gasket for connecting the bottom of the catalytic converter to the front pipe of the exhaust system. If you search on ebay for "lancer exhaust manifold", you will be able to find various sellers that sell the front catalytic converter replacement kits.
To replace the catalytic converter, you remove the upstream oxygen sensor, remove the heat shield, and unscrew the 10 or so bolts that connect the catalytic converter to the engine. Then get under the car, and remove about three bolts that connect the bottom of the catalytic converter to the front pipe. The car emitted white smoke at first, but after about 10 minutes or so it stopped smoking.
I have driven at least 1000 miles and the check engine light has not come back on. I also was able to pass emissions.
I hope this helps. I spent countless hours trying to fix this problem, and wanted to share what I learned. If you are getting the p0421 code, replace the front catalytic converter first. Replacing the oxygen sensors is not a bad investment, as it helps maintain good gas efficiency.