A lean code bank two can be caused by a vacuum leak from a vacuum hose or intake manifold that effects bank 2 (ie the bank that does not have number 1 cylinder on that bank). Many automotive repair shops have a machine that generates an inert non flammable low pressure smoke that looks similar to cigar smoke. The intake manifold is sealed off, and smoke is put into the engines intake manifold. The smoke then fills the engines crankcase and if there are any vacuum leaks from gaskets, hoses, or housing smoke emits from the source of the leak. Some mechanics will use propane or aerosol carburetor cleaner, with the engine running they will spray the cleaner or propane around the intake manifold and vacuum hoses. A leak will cause a "lean mixture" condition, when the flammable fuel (carburetor cleaner or propane) comes in contact with the source of the vacuum leak the engine idle speed will raise as the engine has received "fuel". this method of finding a vacuum leak works but is not recommended as it can easily cause a fire.
Lean codes are often falsely set due to an Oxygen senor (or Air fuel ratio sensor ) that is failing, contaminated or gone lazy. Sensor testing requires a scan tool or oscilloscope. When a code is set valuable information is stored in the computer on your car that may require a professional quality scantool to utalize that information. The key information obtained here is it will tell you in a percentage the fuel trim values long term and short term for each bank of cylinders. For example bank one -2% bank two +24% would mean the computer sees it has to add 24% fuel to make the bank two work efficiently.