It depends on what you want to do. To thoroughly air dry for dry storage (not necessarily in a fridge) can take two or three weeks but that should be indoors in something like an open paper bag or cup or something. I wouldn't do it in a plastic bag in the sun or the heat may kill the seeds.
Where things get complicated with daylily seeds is that some seeds have seed dormancy, which means they won't germinate immediately when planted in otherwise suitable germination conditions. This can happen with a percentage but not all seeds of a seed batch. There's no way of knowing before you start whether any given seed will have seed dormancy. What typically happens is that you plant the seeds, some come up almost right away and the others germinate spread out over weeks or months. If this happens then your seeds have seed dormancy.
To get around it, if this happens and you don't want to just wait it out, you can stratify (damp chill) your next batch of seeds in the fridge. This means the seeds must have sufficient internal moisture content for the chilling to break their dormancy and allow them to germinate promptly. We do this by adding some drops of water or a damp kitchen paper towel or coffee filter to the plastic bag or container with the seeds, or put the seeds into a damp medium such as vermiculite, sand, perlite in a bag/container and then refrigerate for about a month. Then, when you take the seeds out to plant them, they should germinate all together within a couple of weeks at room temperature.
We can get conflicting ideas on this because seed dormancy in daylilies is variable. It may be that the climate, the parents, the time of harvest, the time of sowing, the temperature or other factors influence whether an individual seed is going to have seed dormancy. Even an individual specific seed can be dormant at some times in its pre-germination life but not others, for example the dormancy may wear off in long term dry storage so the seed may be dormant if you start it soon after harvest but not if you've stored it for a longer period.
People with daylily seeds that don't have seed dormancy often do not believe stratification is beneficial
. I didn't to start with - the first batch of daylily seeds I started in spring after months of dry storage at room temperature all germinated at over 90% within a couple of weeks of starting. So I decided to prove that they didn't need stratification to germinate that quickly. The next year I started several batches with and without damp chilling, but this time in autumn, and found that the ones started without it did germinate erratically over a long period of time while the stratified ones germinated all together within a week or two. The two main differences were time of year of starting and more warmth and sunlight on the windowsill for the spring started ones.
Where there's a grey area is refrigeration of seeds that have not been thoroughly dried down to the minimum moisture content needed for dry storage at room temperature. The question is do these seeds stratify because they still have enough moisture content, or did they not have any seed dormancy to begin with? Refrigeration of seeds that are thoroughly dried internally does
not break seed dormancy, it is simply a way of storing them for longer.
This is getting kind of long and sounding more complicated than it is! The bottom line is that, if your seeds don't all germinate within a couple of weeks or so of starting, then stratification (damp chilling) in future should make this happen. If you don't mind waiting for the slow ones then you don't need to damp chill them. For the most part they will probably germinate anyway given enough time but this can be a long time. If you're trying to dry them for dry storage at room temperature and not stratifying it will likely take longer than a few days.
It's possible for them to germinate in the fridge but usually it is after they come out to room temperature. I suspect when they germinate in the fridge that they may not have been dormant to start with so the refrigeration was actually unnecessary, but I don't think anyone has researched that.
