Cover a large area with newspaper and set the sawhorses on the newspaper. Lay the lattice on the sawhorses.
Stir, do not shake, the stain before opening to keep air bubbles to a minimum. Dip your paintbrush bristles halfway into the stain. Apply the stain to the lattice in one smooth stroke. Refill the brush as needed. Once the exposed side is stained, wrap the brush in a plastic bag and stick it in the refrigerator to keep it fresh.
Flip the dried lattice to the other side after the stain dries. Remove the brush from the refrigerator and bag. Stain the exposed side of the lattice, paying close attention to the sides of the slats. Wipe any drips or runs with a soft cloth, as they occur.
Inspect the lattice from all directions to find unstained areas of the wood. Touch up any areas you missed in the first application of stain. Store the brush, covered with the bag, in the refrigerator. Allow the lattice to dry completely.
Apply another coat of stain, if you desire, to achieve the color you want for your project. Cover the entire side each time you apply a coat of the stain to keep the color consistent throughout the latticework.