Can you lay sod in a shady place?

Yes, but it may thin or even die if it gets very little direct sunlight. If it does survive it probably wont stay as thick as when it was new sod. Choose non-netted sod if you give it a try so if it does die or thin you wont have netting showing up. I have better luck with sod in shade than seeding as the germination is normally poor in this situation.