Melt butter in a large saucepan over medium heat. Add potatoes and onion, cook stirring occasionally until onion is tender, about 5 minutes. Add flour and cook stirring constantly for 2 minutes. Gradually add milk and broth, Bring to a simmer and cook until potatoes are tender, approx. 10 -15 minutes, stir occasionally. Add broccoli and cook until broccoli is tender about 5 - 8 minutes longer. Remove from heat and stir in cheese. Add lemon juice, season with salt and pepper.