Then the lambda sensor wasn't faulty! Didn't they test the sensor to see if it was working?

Let's start with the obvious: is there a leak in the exhaust upstream of the cat? Partial vacuum pulses at low load can draw air into the exhaust confusing the lambda sensor.

Failing that, is there a consistent misfire in one of the cylinders? This would pump air and fuel into the exhaust, again confusing the lambda sensor. Take the plugs out and examine the tips-they should all be tan brown. If one of them has a very different colour to the others-that cylinder has a problem.

Moving further upstream, the fuel pressure regulator could be faulty (unlikely) or the MAF could be dirty/malfunctioning.

No, changing ther air filter will not help matters!

It's disappointing that the garage assumed that the lambda sensor was faulty simply because the readings were out of range.

A very typical example of a garage that does not have a clue about engine management systems. Sadly they are not alone either. They plug in the scanner and there's a mention of lambda sensor. They take this as gospel and assume it's faulty, whereas in fact the sensor is reading correctly telling the story as it is, and the fault actually lies eleswhere.

The oxygen sensor on your car contains zirconia which is a substance which is sensitive to oxygen. As oxygen passes the sensor small voltage is produced. The more oxygen the higher the voltage. The sensor actually compares the oxygen inside the exhaust with ambient oxygen outside. Since a richer mixture consumes more oxygen than a lean one If there is little difference (low voltage) the ECU knows the mixture is rich. If the difference is high then it knows the mixture is lean. Prior to this the ECU needs to know engine speed and position, throttle position, mass air flow for load and the temperature of the intake air as well as engine temperature. With this information it can calculate how long to keep open the fuel injectors to provise the precise quantity of fuel for all engine conditions in real time. Longer injector duration means more fuel injected, and shorter means less.

The oxygen sensor will continuously switch from low to high and back (0.1v - 1v) as the ECU richens up and leans off. This cycling is known as 'Closed Loop'. If the engine is running badly because of a misfire due to a faulty spark plug or coil, or incorrect valve clearance, air leak, fuel pressure fault etc then the closed loop system will not happen. The sensor readings will be erratic and a fault code relating to the sensor may be generated. This does not mean that the sensor itself is faulty.

Most oxygen sensors have 4 wires. 2x white which are a 12v supply for the heater circuit and ECU supply voltage. Black which is earth and grey which is the signal return to the ECU. Use a voltmeter to see what the sensor is doing by probing the grey wire and earth. As I mentioned earlier you should see a continuous rise and fall between 0.1 and 1 volt DC.

Hmm. You say it is running rough at idle, what about under load?

Are all of the spark plugs fed by the same same coil pack (if it isn't a distributer)? I wonder if a weak spark is causing misfiring. That would explain blackish wet plugs.

Does the exhaust smell 'fuelly' ie is it obviously running rich (although misfire can also make an exhaust smell of fuel)?

I'm betting this problem is simple and well within the bounds of a DIY mechanic.

Ah, coil on plug-so it's a bit newer than I thought-I must have been thinking of the old liberty.

Well, since they have their own coils, they are unlikely to all be misfiring. The MAF is situated upstream of the throttle body. You could try cleaning that next!