I was having this exact same issue with my 2007 Silverado. Service stabilitrak light would come and go, mainly at low RPMs and go away when the RPM's rose.
I found out that the problem was an exhaust leak at the flange between the manifold and catalytic converters. This was causing the lean code and triggering the service stabilitrak. I patched that up and it has been running great since.
The important thing here is to know which bank is being triggered. If it is both then it is probably up by the intake. If it is one or the other it is either a sensor or an exhaust leak. This, of course, is just from my experience.
Hopefully this helps someone with the same problem!