Melt the butter in a saucepan over medium-low heat. Add the onion and cook gently until softened but not browned, 5 to 10 minutes.
Stir in the potato, then cover and cook gently for 10 minutes, stirring from time to time so that the potato doesn’t stick to the bottom of the pan. The potato won't be tender quite yet. Remove the lid, add the stock, and season with salt and pepper. Bring to a boil, re-cover, and gently simmer until the potato is tender, 10 to 15 minutes more.
Add the lettuce and herbs to the pan and cook just until the lettuce has wilted. Turn off the heat and let the soup cool slightly. Purée the soup with an immersion blender or in a standing blender (working in batches if necessary) until smooth. Taste and adjust the seasoning accordingly. You can sip the soup either hot or cold, so either return the soup to the pan and gently rewarm over low heat or cover and refrigerate until chilled through. (To freeze the lettuce soup, let it cool completely and freeze it in individual resealable plastic bags for up to 2 months. Reheat the soup in a covered saucepan over medium-low heat, stirring frequently, until warmed through, 15 to 20 minutes. Alternatively, nuke the soup in a covered bowl in the microwave on full power, stirring several times, until warmed through, 7 to 8 minutes.)