Some people do soak orientpet lily seeds in water first, and claim beneficial results. Others don't. But as a general rule, soaking lily seeds is not needed or done. I meant to wet the seeds at that very moment, only so they would stick to the bottom of the baggie, and stay put while you fill it with the peat/vermiculite.
Perlite is just fine to use, but don't use it exclusively when germinating seeds. Since perlite does not absorb water, and only holds a small amount on the outside of the granules, it would be very difficult to maintain the correct moisture level for any length of time. Adding peat or vermiculite alleviates the problem. Seed starting mixes are soiless, and are usually composed of peat and vermiculite, and sometimes perlite too. Your media should be just fine, Lily.
Regarding your mini fridge, since you have bulbs in there the coldest temp would be 33F. Dry lily seeds in storage last the longest in a deep freeze. Even zero degrees is fine. Seeds could easily be kept for 10 years this way with no loss of germination. Keep the freeze/thaw cycles to a minimum.
"My" method is really not mine. Even the sticking wet seeds to the bag was adapted from someone else.
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Caroline, that's good advice you are giving yourself:
I'll keep them through another winter if no results this spring.
Sometimes seeds are just stubborn, and we can't mimic mother nature to their satisfaction. So another year under her care is a good plan.