Lav+/lav x lav/lav (did I write those correctly?) would produce 50% lavender and 50% non-lavender. It doesn’t matter what has already been produced. It’s a possibility that not all your silkies carry lavender, either.
I don’t have much experience with silkies, but from what I’ve seen of threads asking about what color silkies they have, it can be hard to tell the difference between partridge, silver partridge, and blue partridge. I could be wrong, though.
The blue rooster doesn’t have two copies of the barring/cuckoo gene, so he won’t produce all cuckoo offspring. As he’s a mix and you aren’t 100% sure on his parentage, it’s hard to be certain of what genes he could have. He could have duckwing or partridge genetics which could be passed on to his chicks.