A general rule of thumb is to cross like with like. So asiatic with asiatic and oriental with oriental and so forth. Tiger lily is considered an asiatic lily. Some of the interspecifics are fertile with tetraploid pollen. For example, I can get good seed from the orienpet lily American West using tetraploid trumpet pollen. But the interspecific lilies themselves (for example, oriental x trumpet lily) are created through laboratory embryo culture procedures.
This is really a simplified explanation. For any cross you consider you can post on the lily forum here for comments from the peanut gallery. There are a few of us here with at least some experience in producing seeds.
One piece of advice I would like to give is to not try to set too many pods on one plant as seed making is a great drain on the bulb. Too many pods can mean a weak return the following season of your pod parent. I learned this the hard way! I usually do just one pollination on a small plant (maybe only 3 or 4 blooms available) and up to 3 on larger plants, say for example, a well budded trumpet lily.
Here is a link to an article describing the different divisions of lilies. Lilies within a division can be compatible for crossing (though not always):
http://garden.org/ideas/view/p...
