Albino x Albino = Offspring no Albino
For the above crossing and the off-spring produced, does it
indicate that Pigeon-Blood lineage in the Albino is absent?
Taken that the brown-based parent, which can be any fish i.e. LSS, RSG.., possess no pigeon-blood genes, then if all off-springs turn out brown for more than 1 batch of fry, it sort of indicates that there is no pigeon dominance in the fish. It can be a safe assumption that chances are that the albino doesn't contain any pigeon genes.
However, crossing a brown to a 'melon' (Pigeon Blood), woul dstill give a certain percentage of phenotype brown (i.e.with stress bars 'n inner breeding bends), which makes the above assumption not 100% in accuracy.
Someone had a snakeskin for sale in the online classifieds, and had mentioned the presence of a certain percentage of Pigeons in his batch of off-spring. However, both adult fishes does show stress bars, which are traits that inherently isn't pigeon-blood. It is assumed that either or both of the parent snakeskins (bot of which exhibited the non-pigeon phenotype) has genotypes constructed partly by the pigeon-blood gene.
Therefore based on this example and theoretical basis, there is no way to tell that a brown is just a brown (just like the debate over whether a golden is really just a golden without the pigeon-blood genes).
In this light of analysis, if we are able to see (whcih of course we aren't able to) whether the albino is brown or pigeon, we cannot really tell for sure because if we (of course again, we're not able to) are able to see the stress bars of the albino, strongly indicating that it hadn't descended from the pigeon blood strain, and going by the above theory - again, we cannot be certain.
Looking at the example of Brown Based x Albino = Offspring Browns again, i suppose one such crossing is not enough to prove that the albino is not of Pigeon-blood gene, because if the Pigeon-blood is already very much in a lesser proportion of the genetic make-up of the albino (eg.**), then crossing it to a brown non-Pigeon blood fish might further dilute the Pigeon blood gene in the albino, and thus causing the Pigeon blood to loose phenotype dominance in the F1 of such a crossing.
eg.** (the possible dilution of the pigeon blood gene in an albino in the process of crossing for a pigeon blood albino)
Pigeon x Albino = F1
F1 x Albino (which might be a brown albino = F2 of this crossing (fish in albino state)
As for Albino x Albino = Offsping no Pigeon Blood phenotypes, we cannot be sure, simply because Albinism is a defect, which many might term as a disability too. It does affect the pigmentation build-up of many genetic structures, and hence in the process causing a massive change in phenotype/physical appearance. It is due to this phenotype disparity that many of us might deem a great genetic change in dominance in the fish, but that is really genomes, and much of genotypical structure that we cannot deduce just from the phenotype of the off-spring.
Therefore, even if both albino parent fish are dominantly pigeon-blood strain with many many black speckles/freckles (which can only be seen if the albinism isn't there), crossing both would render all the off-springs to be albinos - in which the state of albinism would still be preventing us from seeing the pigeon-blood gene, which strain can only be recognised from the phenotype of a fish - and in this case, the albinism masks it.. yet again.