Here's a more complete explanation, for the good of the thread.
The raster data model is based on a single value per cell for most operations. If you want to preserve attributes on the raster side, these suggestions are right on - specify the ObjectID field as a "Value field" for the Polygon To Raster tool, and then copy the polygon attributes over to the raster attribute table using the Join Field tool.
However, for analysis purposes with raster tools like the Raster Calculator, it really does make sense to convert to raster using the field you will be analyzing. (The Lookup tool may be used in map algebra to access attributes for calculation purposes, but is generally more convenient and efficient to not have to use it.)