Assuming that last group of offspring is all similar, then you would be on your way. But, one generation of all similar offspring would not prove it is a strain. I would venture that a minimum of 3 or 4 generations (being all similar) would be needed. Something else Brian Bergman said that I neglected to say before: It is not uncommon for hybrid lily offspring to "suddenly" show strong alliances to one of their grandparents, even though no such characteristics were observable in their parents.
Take, for instance, the case of a hybrid from two heirloom corn strains (all seed grown heirlooms would be strains). Because there is so little variation within each heirloom strain, one might expect that the genetic combinations of the offspring would be very limited. And they are. The progeny are all the same. This is exactly how hybrid corn seed is produced. So each of these hybrid corn plants are (outwardly) the same, but we can't expect that if we crossed them, similar offspring would be produced. In fact, this is not the case at all. The offspring of hybrid corn are not similar.
Jumping to lilies, the analogy is not so cut and dry, because corn only has 20 chromosomes and lilies have more (actually 24), but it still holds. Species lilies (species anything) will have more diversity than heirlooms, as heirlooms are effectively inbred (at least those that are reproduced by seed). Still, you will see somewhat similar results. The F1 generation of a species cross will have some variation, but not nearly as much as the F2 or F3 or more generations.
Genes are sometimes predictable, and sometimes not.
