02TTR0@dstr

Hey guy, I'm need to the forum and new to audi, I recently bought an 02 TT 1.8T roadster from a family member, I bought it cheap because it had an idle issue that he couldn't figure out, when starting the car, it idles fine for about a minute, then the idle gradually begins to bounce between 500 to 1300 rpm, when you unplug the vacuum hose/ non return valve from the top of the charcoal canister, it returns to normal idle immediately, if you plug it back in, the idle gradually starts pulsing again. Also is throughing a bank 1 lean code p0171, the car has 154,000 miles
ANY help or advice would be appreciated!! I'm new to these cars and still leaning, thanks!