Place the milk and water in a large saucepan with salt and sugar. Heat over medium-high until it comes to a boil. Whisk in the grits, then reduce the heat to medium-low, and stir and simmer until the grits are thickened and tender, about 25 to 30 minutes. Turn off the heat, and whisk in 4 tablespoons of the butter.
Place the remaining butter in a skillet over low heat to melt the butter. Stir in the brown sugar, honey, blueberries, lemon juice, and cinnamon, and cook until the sugar melts and the berries are warmed, about 2 minutes.
To serve, spoon the grits into bowls, and top with the warm blueberry mixture and toasted walnuts.