In a bowl, combine 1/3 cup fresh lemon juice, melted butter, dried thyme, garlic powder, cumin, and red pepper flakes.
Generously rub the lemon juice mixture over the Cornish hens.
In another bowl, mix 1/2 teaspoon ground thyme, salt, and black pepper.
Sprinkle this herb mixture evenly over the Cornish hens.
Pour chicken broth and 1/3 cup fresh lemon juice into a slow cooker.
Place approximately 1 tablespoon of chilled butter cubes in the cavity of each hen.
Set the hens in the slow cooker and arrange the remaining butter cubes in the chicken broth mixture.
Cook the hens in the slow cooker on High for 4 hours or on Low for 8 hours.