They may not be accustomed to sunlight, so that might have caused a problem, but the main issue is probably lack of water. Water when the surface of the soil feels just about dry to the touch, water well, allow to drain down freely. Check them daily to see if they need water, especially if the weather is hot and sunny, when they might need watering twice a day because the pots are small. Acclimatize them to sunlight gradually, but the parsley may do better in partial shade anyway.
The lavender needs a larger pot so find one the next size up and move it into that; use new potting soil to put round the root ball and water well when it's done. You will probably need to cut off the parts that have died back, right at the base of the stems close to the soil. The Basil is okay at the moment, but will likely need a bigger pot soon, as will the peppermint. Moving them out of the rain is not necessary, unless it's raining so hard its battering trees and large plants to the ground with the force of it.