Drill a pilot hole large enough for a #12 screw in the concrete wall. An electric drill with a carbide-tipped drill bit or a hammer drill will do the job easily. Pilot holes should be drilled at 3-foot intervals, vertically and horizontally, creating a grid of holes in the concrete.
Install plastic anchors that will accommodate #12 screws in each of the holes. Simply insert the anchor in the pilot hole and tap it gently with a hammer to embed it.
Cut lengths of PVC pipe into 2-inch sections with a hand saw. You need the same number of pieces of PVC pipe as the number of pilot holes you drilled. Using PVC pipe as a spacer between the lattice and the concrete eliminates the need for wood that will rot in a few years and need replacing. Drill pilot holes through the center of each 2-inch length of PVC pipe.
Drill pilot holes in the lattice or trellis pieces at 3-foot intervals, horizontally and vertically. Make sure the pilot holes in the lattice line up properly with the pilot holes in the concrete wall. To do this, you may need an assistant to hold the lattice up against the wall while you mark the location of the pilot holes for the lattice.
Secure the lattice to the concrete wall. Ask an assistant to hold the lattice in place against the concrete wall. Put a 4-inch hot-dipped galvanized screw through the pilot hole in the lattice, then through the PVC pipe and into plastic anchor in the concrete wall. Press the assembly tightly against the concrete wall as you tighten the screw with an electric drill. Repeat this process for each of the pilot holes until all of the lattice has been installed.