Stir in the broth, bring to a boil, reduce to a steady simmer, cover, and cook for 10 minutes. Uncover and simmer until the liquid has thickened, about 5 minutes. Smash some of the beans with the back of a spoon. Stir in the lemon juice and season with more salt, if needed.
Nestle the grilled sausages into the beans and cook gently for 2 to 3 minutes to reheat the sausages and combine the flavors. Serve warm.