To add another DP, I went to book 2 biz seats JFK-LIS on TP via LM the other day. After booking the first seat, the inventory immediately disappeared despite showing 4+ seats initially. I thought it was a LM quirk but when I checked the availability on AC, it had disappeared there as well. I canceled and within 10 minutes the 4+ seats showed up again on both LM and AC. I was then able to book 2 seats under one reservation via LM (inventory again disappeared after that), so it wasn't a phantom availability issue either. I went to book a return on TP via AC and had the same experience.