Nail the lattice to two of the 2x4s, one along the top edge and one along the bottom edge of the lattice panel.
Measure a 4-foot section along each of the landscape timbers or posts where you want the lattice panel to go, depending upon how you plan to secure the finished fence. Mark the top and bottom measurements with a pencil across each post. Whatever you decide, make sure the lattice panel clears the ground by several inches to avoid element exposure and is exactly the same on both posts.
Place the lattice panel from Step 1 face down on the posts, with one post at each end of the panel. Align the panel with your post markings and attach the panel to the posts with screws through the 2x4s.
Cut the third 2x4 in half and place a piece on each end of the fence between the top and bottom 2x4 frame. Attach them to the frame with screws into the posts.
Secure the fence as you choose and introduce your climbing plants to the lattice.