In Tibetan Materia Medica Vaidurya is not lapis lazuli , it is sapphire, and more specifically star sapphire (which accounts for the checkerboard pattern of the ground in refuge visualizations.
There are blue, white and yellow Vaiduryas. There can never be a white or a yellow Lapis.
Lapis on the other thand is very clearly the stone called mu men (མུ་མེན). Please consult འཁྲུངས་དཔེ་དྲི་མེད་ཤེལ་གྱི་མེ་ལོན་ -- this is the standard text reference for materia medica used in Tibetan Medical colleges.
Your reference about beryl is possible, but not definitive.
I should also add, that the word is a generic name for gems that are very shiny and catch light in very specific ways, for example, cat's eye (chrysoberyl) is also called Vaidurya.
Here however it is བཻདུརྱ་སྔོན་པོ༷, which is in fact star sapphire, as opposed to the more common indranila, regular blue sapphire.