Heat oil over low heat. Add the onions, shallot, thyme, and salt.
Cook on low heat until the onions begin to brown, stirring occasionally. (About 30 minutes.)
Add the garlic and cook 2-3 more minutes. Remove the thyme. Squeeze the lemon juice into the pot, and use a wooden spoon to scrape all the brown bits off the bottom of the pan.Allow the onions to cool to room temperature.
Optional (for a Creamy Dip): Add the onion mixture and yogurt to a food processor or blender and blend until creamy.
Stir in the chives.Refrigerate the dip at least 30 minutes before serving, or up to 3 days. Taste before serving and add more salt to taste if desired. Serve with vegetables, chips, or other side of choice.