Arrange the chicken in a single layer in a wide skillet or large Dutch oven with a tight-fitting lid. Add the lemon, garlic, and bay leaf. Pour the broth on top. If the chicken is not fully covered, add more broth or water until it is covered by at least 1 inch. Add salt if using water or unseasoned broth.
Bring to a boil over medium-high heat. Reduce the heat to a simmer, cover, and cook until the chicken is tender and fully cooked (165°F on an instant-read thermometer), about 8 minutes.
Remove the chicken from the poaching liquid and let cool completely, then shred. If desired, strain the poaching liquid and use it as a broth in another recipe.
Store the chicken in a tightly covered container in the refrigerator for up to 4 days. Store the strained broth in a tightly covered container in the refrigerator for up to 3 days or in the freezer for up to 2 months.