Make the sauce: In a medium bowl or jar, whisk or shake together the garlic, lemon juice, mustard and salt. Stream in the olive oil, whisking until smooth. Add the Italian seasoning and stir to combine.
Alternatively, add the garlic (no need to chop first), lemon juice, mustard and salt to a blender. Blend on high, then stream in the olive oil and blend until smooth. Add the herbs and pulse to combine. Use immediately or cover and chill for 3-5 days.
Add the chicken along with ½ cup Lemon Herb Sauce to a 6-quart slow cooker.
Cover and cook on high for 3-4 hours or low for 4-5 hours, or until the chicken shreds easily with a fork.
Remove the chicken, shred with two forks, then add it back to the slow cooker, stirring to combine. Stir in the remaining Lemon Herb Sauce, or reserve the Sauce and serve it on the side.
Serve the chicken as is, or use it in bowls, pasta, tacos, salads, stir-fries or mason jar salads.