Mix yeast, sugar, and water in a large bowl. Let sit for five minutes.
Beat in milk, eggs, sugar, oil, salt, and vanilla. Stir in flour a cup at a time, adding enough to get a soft dough.
Knead till smooth. Place dough in a greased bowl and let rest for about 20 minutes.
Roll dough out on an oiled counter to a rectangle about 13x28". Spread melted butter evenly over the top of the dough. Combine sugar and lime zest and sprinkle over the butter.
Roll dough up and seal the edge by pinching. Cut into slices 1" to 1 1/2" thick. Place on greased cookie sheet with sides.
Cover with waxed paper and let rise till doubled, about 45-60 minutes.
Bake at 350° for about 30 minutes or till lightly browned.
Combine icing ingredients, adding enough lime juice to make a thin icing. Spread over warm rolls.