In a large mixing bowl, combine the warm water, quick-rise yeast, and sugar. Stir gently and let it sit for about 5 minutes until it becomes frothy.
Add 1/4 cup of the melted butter to the yeast mixture and stir to combine. Reserve the remaining melted butter for later use.
In a separate bowl, whisk together the all-purpose flour, salt, and Lawry's seasoning garlic salt.
Gradually add the dry ingredients to the yeast mixture, stirring until a shaggy dough forms. Knead the dough in the bowl until it becomes smooth and elastic.
Cover the bowl with a kitchen towel and let the dough rise in a warm place for about 30 minutes, or until it has doubled in size.
Preheat your oven to 375°F (190°C). Once the dough has risen, punch it down and divide it into about 12 to 16 pieces. Roll each piece into a long stick, about 6-8 inches long.
Place the shaped breadsticks on a greased baking sheet. Brush with the remaining melted butter and sprinkle with grated cheeses.
Bake for 15-20 minutes, or until golden brown and the cheese is bubbly.
Remove from the oven, let cool for a few minutes, and serve warm.