Using a lavender split in BBS is a bad idea. Any time you introduce a recessive gene it can pop up later and create real headaches, and I think even more so if it's mixed with blue. Some people still confuse the two to begin with, and I can see her selling blue chicks as lavender and lavender chicks as blue.
Also, with lavender being a new variety that still needs a lot of work, we're crossing to black to improve them because the blacks are much better. So if you take a line of BBS and add in bird that comes from lavender, you're taking a step backward, because even though it's visually black, it's still descended from birds of the lavender variety that need a lot of improvement, as opposed to birds from the black variety that we're using to do the improving, if that makes sense.
Lavender is recessive, so a bird carrying only one copy of the gene will be visually black. A bird carrying one copy of a recessive gene (lavender, recessive white, etc.) is a split. Blue is dominant, so if a bird carries one copy of the gene, it will be visually blue, and if it carries two copies it will be splash. A visually black bird from a BBS mating would not carry any copies of blue and therefore wouldn't be a split.
Hope I haven't given you an eye-twitch, lol. If you really want to get one, here's a thread to check out:
http://ameraucana.org/forum/index.php?topic=1733.0
