I actually read that seedlings of some lilies are not particularly fond of being baked by strong sun , so I think they may need some shading. If there is not too hot and too dry you can just as well plant them now, then they have more time to establish themselves before winter.If they are supposed to be hardy in your zone they will survive. Soil not too rich, especially some salts I do not recall names at the moment. Well drained is important, best in a raised bed.

If you get one of those polystyrene boxes used for shipping grapes that are about three inches deep, about 12 wide x 16 long you can add extra holes - about as fat as a finger - and then put in around an inch of potting medium over the bottom.

Mark out a grid pattern so you end up with three across and four down the length - 12 seedlings in all. You can do a row and fill as you go. Fill up to nearly the brim of the box and water lightly. You can add about half a measure of sharp grit to four measures of potting mix.

Or you can plant your seedlings individually into 6" pots at this stage. Later they will need something larger, however.

Lilies aren't partial to superphosphate. They get brown bits on their leaves from the fluoride.

Many of the lilies have a set of basal roots which store the food for them to get started in the new season.

Once they get growing, though, they form stem roots ABOVE the bulb. That's why they get planted quite deeply. It's those roots that support the stem, leaves and buds.

When they come up next year you can use a sparing amount of slow release fertiliser to help them grow on and form bigger bulbs.

You might not see flowers for three years.

As the bulbs get larger you might want to plant them out into a special area free of perennial weeds. They like the edges of deciduous shrubberies/woodland for the dappled light and leaf mould but they don't like to compete with surface roots from trees such as maples.

Congrats on your seedlings. I've tried WSing them for 2 season with no success. Can you tell me are you using potting soil, if so did you add fertilizer?