For germination to happen, moisture for the seeds is more important than sunlight. So if you merely pressed them into the surface of the soil, I suspect they were too dry. Shadecloth doesn't really hold in moisture, because it allows ventilation (and gee, it even blocks light!) You'd need plastic sheeting to hold in moisture. Lettuce likes light to germinate, but the usual rule is to plant 1/8" deep. As in, under soil, but not under a lot of soil.

I don't grow a lot of lettuce, but when I did, that was how I did it.

I grow lettuce in a clay pot; seeds scattered on the surface, covered with tulle and watered every day. Maybe the lack of moisture is a problem.

Sprinkle seeds on soil, preferably in rows so you know them from weeds. Use your hands to lightly smooth some soil over them. Water as often as needed to keep them continually wet, especially overnight and in the AM. They need cool temperatures to germinate (40-60F).

lettuce doesn't need sunlight to germinate. moist soil at a temp of about 75F works good. as soon as it sprouts it needs light.

Your soil surface may be too warm for germination. The dark soil often heats up in direct sunlight much more than the air and can inhibit germination. Try shading the area, or start transplants out of direct sunlight where soils temps will be more moderate.

And keep the soil moist and cover seeds lightly as others say.

I had lettuce growing wild in my yard in Venice, and it seemed to grow mostly in the winter. I planted a lot of seeds yesterday, but not lettuce - mostly parsley (which I already have growing), sorrel, lemongrass, cilantro, dill (which I also have, but I want more), and chilies. I start the chilies and lemongrass indoors, but the rest I planted outdoors, although I planted some sorrel seeds indoors as well. I also planted some cabbage because it was a free gift from the seed company, but I would have preferred lettuce. Normally I buy small lettuce plants instead of seeds.

Thanks for all the comments! It turns out that the day after I posted this my lettuce seed did sprout, which I was surprised at. Now I have a bunch of very tiny seedlings that I need to make sure don't die. Since a lot of them were scattered on the surface they are having trouble rooting. That's lesson number one. If I covered them a little bit they would be less likely to come loose when I water. It would probably also help keep them more moist, although the soil seems plenty moist to the touch. My setup is similar to lgteacher above although it is a raised bed instead of a single pot.

I understand that many people sow lettuce directly but I have had much better luck sowing it in six packs. I put several seeds in each cell, and vary the variety by six pack. Once the seeds have sprouted I prick them apart and transplant, a cell or two at a time. Then I wait two weeks and do another cell or two from each variety, and so on until I've exhausted the supply. They barely grow in the six packs so this way I stagger the plantings and have lettuce for a much longer period of time than if I sowed them in the ground all at once. And my germination and survival rate is close to 100%.