I think it really depends on what AC has available on that codeshare. Or what/how they have negotiated to share with LH.
Rando dates on AC.com for random route. YULTXL. 3/4/5th of June gets dumped in Y. 6/7/8/9th of June gets P. 10/11th is Y. 12/13/14th gets P. 874 to 9119.
Considering LH has more than one partner connecting to that specific flight with J pax, I can see them protecting their J inventory for their own sales and limit the partner connections in J.