Well, the typical failure mode that causes this on the Bonnevilles is a bad fuel gauge sender unit, usually located on top of the fuel tank by the fuel pump (for Bonnevilles - probably similar or the same in the Lumina).
Usually, if not fixed, the gauge will eventually stop working completely. Many times the sender failure indicates other problems up there too, like rust.
Point is, you need to take a good look up under there and see what you can see.
Search on "fuel sender" or "bad gas gauge" or similar terms for threads dealing with this.