To trace the lines onto polygons, try using the Integrate tool:
Compares features and makes any lines, points, or vertices within a certain distance range identical or coincident.
To match the attributes of the polygons to the lines, you can use the spatial join by @wittich or other similar methods described in Match features that are spatially similar with ArcGIS?Match features that are spatially similar with ArcGIS?.
Since you're on 9.2, unfortunately you won't have the Conflation toolset.