If using bacon, cut into ½-inch strips. Saute in a Dutch oven or a similar large, sturdy pot over low heat, until the bacon is crisp and the fat has rendered, about 10 minutes. Transfer to a paper-towel lined plate; discard all but 2 tablespoons drippings from the pan. If using a ham hock or ham bone, melt the butter over medium heat, then proceed with the recipe.
Add the onion to the melted butter (or bacon drippings). Increase the heat to medium. Cook, stirring occasionally, until the butter melts and the onion begins to turn translucent, about 5 minutes.
Add the carrots, celery, salt, and pepper. Cook and stir for 2 minutes more.
Stir in the garlic and split peas. Let cook 1 minute.
Add ham hock, bay leaves, thyme, salt, pepper, and broth.
Increase the heat to bring to a boil, then reduce the heat to maintain a steady simmer. During the first 10 minutes, keep an eye on the soup and with a large spoon, skim off and discard any foam that rises to the surface.
Let the soup simmer uncovered until the peas are soft and starting to fall apart, about 1 hour. If the soup looks dry, add water as needed.
Fish out and discard the bay leaves. Remove the ham hock to a plate and shred with two forks. Discard the bone.
With an immersion blender, puree the soup until it's somewhat thickened but still has some texture (alternatively, you can carefully transfer a few ladlefuls to a regular blender and puree, then stir back into the soup—be careful and do not overfill the blender; hot soup spatters in a blender).
Add the shredded ham (or bacon) back to the pot. Stir in the lemon juice. If the soup is thicker than you would like, stir in additional water as needed to reach your desired consistency. Taste and adjust the salt and pepper as desired (you may want another few pinches of salt depending upon your broth). Enjoy hot.
Notes
To use bacon, cut it crosswise into 1/2-inch strips then begin the recipe by sautéing it on low until the bacon is crisp and the fat has rendered, 8 minutes or so. Remove to a plate, proceed with the recipe as directed, then stir back into the soup at the end.
TO STORE: Place leftover soup in an airtight storage container in the refrigerator for up to 5 days.
TO REHEAT: Gently rewarm pea soup in a Dutch oven on the stove over medium-low heat until hot. You can also reheat this soup in the microwave.
TO FREEZE: Store soup in an airtight, freezer-safe storage container in the freezer for up to 3 months. Let thaw overnight in the refrigerator before reheating.