I'm of opinion Blue and Lav should not be mixed. You'll run into difficulty wondering if a bird is Lav or very pale and non laced blue. A very pale non laced blue is a DQ. Lav is Lav. See what I mean?
Blue must be guarded against losing lacing. Most breeds of blue are in need of improved lacing. If you want to breed blue then by all means do it. I would not be crossing them with Lav. If you found a good quality body type black from a blue flock there is no reason not to use it. I suggest a true black variety as the body type, conformation to SOP will be better than you'll find in the Blue variety. This all is on supposition body type and working toward the Standard are a goal of yours.
The main point is Blue and Lav are not one in the same. Completely different gene. Blue must be laced. A non laced blue is not a Lav, it's simply a very poor quality blue. You have Lavender already. If you got a hold of nice Black stock you'd have diversity of color and be improving your Lav not only in color but body and tails.