> Are you sure there wasn,t a working collie loose on the farm,
That's a point..... I wonder if the litter was dual-sired?
With regard to Tia then yes a Lab father could have produced Tris to a Tri mother. I believe many Labs are Dominant Black [K] but there must be some that are recessive black, as evidenced by the Black & Tan Labs that turned up in a litter a few years ago - this couldn't have happened with the K gene. Or perhaps he wasn't 100% Lab himself.
Collie white markings seems to be passed on very variably, with some collie crosses having none or very little - my family's own Lab x Collie had just a white snip on her muzzle, a white locket and one white foot if my memory serves me correct. [Didn't see any of her littermates but we were told by the [disgusted!] breeder that her mum was a "prizewinning" (aren't they all! lol) show Lab, and dad was the local farmer's collie... in the days before Alizin!].
Thinking about the litter my BSD cross came from (mum was farm bred collie) none of the litter had anything like what I'd call "collie" type white markings - but all 6 had typical BSD white fore or hind toe/s and/or chest spots.