The red one is ruby (variety of corundum – http://www.gemstonebuzz.com/corundum).
Lapis Lazuli is a rock which is mixture of several other minerals and does not occur transparent. With a quick glance, it definitely looked like a lapis lazuli with white veins as calcite (http://www.gemstonebuzz.com/calcite) and yellow minierals as pyrite (http://www.gemstonebuzz.com/pyrite). Is yellow mineral shiny and metalic in lustre? Since, you have said the blue stone is transparent so it is certain that it is not lapis lazuli but can be Afganite as it occurs transparent as well.
However, I will not be able to ascertain blue gemstones unless checked with gemological instruments like refractometer.