In a large bowl add warm water with 1/3 cup granulated sugar and yeast. Stir to combine and set aside for about 5 minutes until mixture is bubbly.
Add 2 cups of flour and mix together with a wooden spoon or dough whisk.
Add an additional 1/2 cup to 1 cup of flour along with the salt, mix well. Add more flour 1/4 cup at a time until dough comes together to form a ball.
Place dough onto a lightly floured surface and knead for 3-5 minutes, adding more flour 1 tablespoon at a time as needed.
Grease a large bowl with butter and place the dough into the bowl, turning it over to grease the top. Cover with plastic wrap and place in a warm place to rise for one hour or until doubled in size.
Make the lemon sugar filling: Zest 2-3 lemons and add a cup of granulated sugar. Mix together with your fingers until well combined. Set aside.
When dough has risen, punch it down and knead out the air bubbles on a lightly floured surface. Roll into a rectangle, about 12 x 6 inches. I usually end up with more of an oval than a rectangle, it doesn’t have to be perfection.
Spread softened butter onto the dough in a thin layer.
Sprinkle lemon sugar over the dough in an even layer and gently pat into the dough.
Use a pizza cutter to cut into 1 inch strips.
Roll the strips into a sweet roll shape.
Place rolls about 2 inches apart into a greased 9 x 13 baking dish.
Cover with plastic wrap and set in a warm place to rise 30 minutes to 1 hour.
Preheat oven to 375°.
Bake sweet rolls for 15-18 minutes until lightly browned.
Remove rolls from the oven and place the pan on a wire rack to cool slightly.
Make the cream cheese icing by mixing softened cream cheese with lemon juice and powdered sugar. Beat with an electric mixer until smooth.
Spread icing onto warm lemon rolls. Garnish with additional lemon zest if desired.
Serve warm or at room temperature.