The first step the correcting the issue is to find out what model this is. I'll assume it is a 3.0i

The second thing is to note that o2 sensors do not usually fail and cause lean or rich mixtures. The software in the DME can detect if there is a lazy o2 sensor and set a fault for aging. Replacing the o2 sensor will only cause the mixture values to adapt faster to a malfunction. Do not replace any o2 sensors for this fault. You should really only replace o2 sensors if they have aged faults.

If you have access to BMW software, read the entire fault memory. On M54 engines, a faulty engine wiring harness can cause lean/rich mixture faults, but will show transmission failsafe/ dsc messages also.

Then make note of the mixture values, so afterwards you can determine if your repair was successful or not.

If you get values such as this, and have not had the car worked on recently or have not reset adaptations

Bank 1 Additive 0.00ms
Bank 2 Additive 0.00ms
Bank 1 Multiplicative 0.00%
Bank 2 Multiplicative 0.00%

There may be a very large air leak, or a faulty air mass sensor.

If you get something like the following

Bank 1 Additive +0.34ms
Bank 2 Additive +0.20ms
Bank 1 Multiplicative -1.00%
Bank 2 Multiplicative -2.50%

It is almost impossible to have a lean mixture at idle and have a rich mixture off idle(above 1300rpms)

This usually indicates a faulty air mass flow sensor, but you should smoke the intake system to check the throttle body boot.

If you get something like this

Bank 1 Additive 0.30ms
Bank 2 Additive 0.25ms
Bank 1 Multiplicative 2.50%
Bank 2 Multiplicative 6.50%

This is usually caused by a faulty valve cover. There is probably a crack between cylinders 4-6. This can be confirmed with a smoke test.

If you get something like this

Bank 1 Additive 0.30ms
Bank 2 Additive 0.25ms
Bank 1 Multiplicative 4.50%
Bank 2 Multiplicative 5.50%

This is usually caused by a leaking DISA or engine oil separator return hose. This can be confirmed with a smoke test.

If you have no other faults beside o2 sensor faults, and you smoke the intake system, and have no external air leaks, and you test the crankcase ventilation system for proper operation, then most likely the software in the engine computer is faulty and should be updated. There is a bulletin that describes this situation.