Take them off the heating! I'll wager that pad is hovering around at least 80 degrees if it doesn't have a thermostat. Mine said it was suppose to be 70-75 and it heats the soil to 85 if the flat sits directly on it. Of course, it will depend somewhat on the ambient temperature of the room, too.
If your seeds disappear after planting, then they rotted. Even if they don't actually germinate, they should plump up. I tried in vain practically all winter one year, attempting to get germination of L. speciosum var. rubrum at variable 68-70 temperature. To make a long story short, they finally germinatied when I moved them to 60-62 degrees. I didn't make a point of it, but they were exposed to indirect light.
Pards right: you may not have viable seed to begin with. if you still have any unplanted seed, see if you can candle them. The embryo is easy to see in this species.
I always start with being very stingy with water if I am starting seeds in baggies and I can monitor the seeds' progress. If the seeds plump, there is enough water. Too much water might actually prevent germination (as well as promote rot), though they seed will still plump. I have had no germination with some seeds (other lily spp.), until I opened the bag and let the medium dry a little.
