I don't think that by means of only single restriction enzyme you would expect to find polymorphism specifically when you intend to investigate only one gene.

There are some critical issues that you have to settle before carrying out the experiment: (1) Is the LALBA gene polymorphic enough to yield patterns of variation? (2) Does the restriction site of the used enzyme (EcoRI) bare mutation hot spots within the analyzed fragment?

I would advise you either direct sequencing or choice of more than one enzyme that would allow to detect variability (or diagnostic enzymes). If  published sequences of the gene in question do exist in gene bank, you could apply RestrictionMapper on them and try to identify the suitable enzymes that could enable you detecting polymorphism within the gene. On the other hand, if there are no clear signs on hot spots variability within the gene that can be revealed by one or two enzymes (diagnostic enzymes), I would suggest that you choose different enzymes whose restriction sites could cover the whole sequence and which revealed signs of polymorphism; by doing so, you could increase your chance of finding variation patterns.

I hope this could help, good luck!

in an outbred population this would just be a rare polymorphism but I assume with sheep there has been much inbreeding from the best ram who possibly has the non cutting allele. It is possible also that the flock is inbred for a high incidence of a second polymorhism which destroys the enzyme cut site so that the normal sequence does not cut but neither does your polymorphism because it is in linkage disequilibrium with a second ,close by,polymorphism. Were they homozygous cutting or heterozygous?