Nope, Lavender is not just double dose of blue. The Lavender gene is a different gene.
Two copies of the blue gene in BBS genetics will produce a Splash bird. One copy of the blue gene will produce a blue bird. The blue gene only affects what would have normally been colored black and does not...
Yes, the Lavender (aka...self blue) gene differs from the blue of BBS (blue, black, splash), also I believe the Coronation Sussex does use the Lavender.