Proof the yeast by stirring it with 1/4 tsp sugar into warm milk (105-110°F). Let sit for 10 minutes until foamy.
Mix the proofed yeast, melted butter, and eggs in a stand mixer bowl. Add flour, sugar, and salt. Using a dough hook, mix on low until combined, then knead on medium speed for 5 minutes.
Rise the dough in a greased bowl covered with a towel in a warm spot for 1 to 1.5 hours, until doubled in size.
Cook strawberries, sugar, and lemon juice in a saucepan over medium heat. Mash berries as they cook. Mix water and cornstarch, add to berries, and cook 2-3 minutes until thick. Refrigerate until completely cool.
Roll the dough into a 14x18 inch rectangle on a floured surface. Spread cooled strawberry filling evenly to the edges.
Cut the dough into 12 strips (1.5 inches wide). Roll each strip away from you and place seam-side down in a greased 9x13 inch pan.
Proof again by covering loosely with a towel and letting rise 45 minutes to 1 hour, until puffy and touching.
Bake at 350°F for 25 to 30 minutes, until golden brown and a toothpick comes out clean.
Make the glaze by beating cream cheese and butter until smooth. Add powdered sugar, lemon zest, and milk. Mix until creamy.
Glaze the warm rolls with the lemon cream cheese mixture using an offset spatula.
