That Purple Prince certainly is scary, but it's so unusually patterned that I would post on the Yahoo lilium group and see what you get there. Just remember to weigh the answers according to their source.
Yes it would be very possible for one stem of a bulb originating from the same plant to be virused and one not. Depending on the type of lily, often divided bulbs will actually break apart while still undisturbed in the soil, and be physically separated. Moreover, a virus does not instantly invade all parts of the plant. There is a time lapse. If one stem was infected one year, you may find that the unaffected stem will be affected next year or the year after. Certainly, viruses travel through growing tissue much more rapidly than not so active tissue, like a basal plate.