Perhaps if you grow lettuce early in spring, you will not need the irrigation nor the shading. I am guessing that snow melt will provide some moisture for a few weeks. Lettuce likes cool weather and is a short-lived crop.

I buy a package of mixed leaf lettuces and plant them in a washtub. I only use a small amount of the seed at one time (there's something like 100 seeds in a packet), so I usually make one packet last a year or so. I use soil-less potting mix. Works better for me than planting out in the garden because I can put the washtub where it gets some shade instead of being in full sun all the time. When the weather gets really hot in the summer and the lettuce bolts I pull it and replant for a fall crop in late summer, replacing some of the potting mix for a fresh start.

Hope this helps,
Edie

I grow lettuce and mesclun in large round bowls on my shaded porch. It's easy to keep watered since I see it every time I go out the door, and when one bolts, I just pull it and plant another seed or two.

We just ate a salad last night from lettuce that I am growing inside under shop lights. No bugs, slugs or bunnies. Definitely the healthiest & prettiest looking lettuce I have grown so far.

I can grow it though most of the summer here if it is planted in the shade of other taller plants, but in containers on the porch is probably your best bet if you are only growing enough for your family to eat.

In the mid-Atlantic, salad tables have kind of caught on, because you can move them out of strong sun if needed. Salad greens don't need a deep root run, so relatively shallow planting boxes work well.

Salad Bowl and Red Sails are easy and somewhat heat tolerant, but I wouldn't limit myself to only those varieties.

In early summer, I often put shade covers over crispy lettuces to buy them a little time.

Here is a link that might be useful: salad tables

A few other ideas you might try are to start indoors and transplant to your garden. Typically plan 4 wks from seeding to transplant; 4 wks from transplant to harvest. Planting on white plastic mulch will keep roots a little cooler.
There are many varieties that perform better in heat. Cherokee is one that is often discussed. I think many Romaine types do better for me in warmer weather. You will benefit from shade cloth and from frequent watering. But even without watering the plastic mulch will hold more moisture and lettuce will produce more abundantly than without it.