Yes, neither is sexlinked, so it does not matter which color is male or female. Lavender is recessive, so it will not show up on the first generation cross to a non-lavender bird that is not carrying the gene, either. So the Lavender bird works essentially like a Black bird on those BBS charts, except all offspring will carry a lavender gene.
How carrying a gene works is, because the gene is recessive, two copies are needed for it to express, one from the mother and one from the father. Since only one is received from the lavender parent, and not from the non-lavender parent, it does not express. But the bird still carries that gene from their lavender parent and thus has a 50-50 shot of passing it on to its own offspring.
It's worth noting that it's not advised to cross Blue and Lavender as it's very difficult to tell which birds have only Blue of those genes expressing, and which have both Blue and Lavender expressing. From what I understand, you just end up with birds that look like a paler Blue with bad lacing when both genes are expressing.
