There is currently no way to run auDNA results (from AncestryDNA, 23andMe, and Family Finder) with the population samples from the research. If the research was publicly funded then I would expect those samples would be publicly available. I also don't know how many SNPs tested by LivingDNA are and are not in common with those from the labs above.
LivingDNA does have a link to download your raw DNA.