Measure the wild rice into a fine-mesh strainer and rinse it thoroughly under cool running water.
In a 6-quart slow cooker, combine the chicken, onion, garlic, carrots, celery, rice, broth, water, bay leaves, thyme, 1 tablespoon salt, and a few grinds of black pepper. Stir just to distribute all the ingredients and seasonings, then cover and cook on high for 4 hours or on low for 8 hours. In the last 10 minutes of cooking, stir in the frozen peas.
Using tongs, transfer the chicken to a cutting board, remove the meat from the bones, and shred or chop it into bite-size pieces.
Return the shredded or chopped chicken to the slow cooker, add the dill, lemon juice, the remaining ½ teaspoon salt, and a few grinds of black pepper, and stir until everything is evenly distributed. Taste and season with more salt, pepper, or lemon juice as desired.