Lean Bank One is a code that should be read up on from the FSM to gain basic knowledge about it. Once you understand that basic stuff you can focus on the true causes.
Serious vacuum leak
Exhaust leak in front of the O2 sensor (manifold or crossover)
You'll notice a few of the items point to fueling (maf, fuel pump), a few point to broken parts that introduce air some way (manifolds, vacuum, egr) and then you come to the last one and probably said... "WTF Bill". Reason being is ...it doesn't make sense that a car can start, run and do all the things your car is doing w/o dimming lights etc and have a battery cable issue. I'm here to tell you though, I've solved this code three times with battery cables. Something about corrosion getting in them etc causes sensors/pcm to be unhappy and you have P0171. Even had a guy in Florida recently that didn't have any corrosion at all (he sliced the coating off the entire cable) and yet.. cables fixed it.
After you pull out your hair.. put a set of battery cables on if all of the easy things don't remedy the problem.
00 Regal GS: All kinds of cool stuff.