Actually, the L. thats found after the Latin name for many species is for "Linnaeus" who was the inventor of the Genus/species binomial system. Species which were given their Latin names by Linnaeus himself have the L. appended. Plants named by other people will have a Latinized version of their last name in place of the L. For varieties or cultivars (varieties are naturally occurring, cultivars are man-bred varieties) you'd have Papaver somniferum var. lacteatum L. or Papaver somniverum cv. something L.

As for the law, all varieties and cultivars of P. somniferum are Schedule II drugs, not just P. somniferum var. lacteatum.

The confusion comes when you consider things like Papaver paeoniflorum. Many botanists consider this to be identical to P. somniferum, and call it P. somniferum var. paeoniflorum. They both have the same chemical make-up, the only real difference is that the paeoniflorums have multi-petaled ruffley flowers that look somewhat like peony flowers. They may or may not count as opium under the law, but since they contain morphine and codeine, they still are illegal to possess without a prescription.