I have a 1998 Lumina with 82k miles, last year the Intake Manifold gasket started to get leaks in it and engine oil was getting inside the radiator.
From what I have heard this is a common problem for a lot of Chevrolet's and the place I took it too says they do these often. I would check your radiator, see if it has oil deposits in the overflow reservoir. When I had it happen to my car, Cylinder 1 and 4 had issues with misfiring so my accerlation lagged, starting was a problem sometimes. Does it have a hard time starting sometimes, not turning over but just engaging period?
It cost me about $700 to get it fixed, tuned up, replaced the gaskets, and flushed the radiator. I hope this is not the issue with yours but if it is be ready to spend some money.