Mark the location for your door. The door should be wide enough to allow a grown person to comfortably access the space behind the lattice. Twenty-four to 30 inches should be sufficient.
Saw through the lattice where you've marked, using the jigsaw. Work slowly to avoid splintering the lattice. Saw through both sides, and the top and bottom if necessary, to free up the lattice. Carefully remove the lattice.
Remove 1/2-inch of material from one side of the lattice and 1/2-inch from the bottom of the door. This will allow you to open and close the door more easily.
Cut 2-inch-by-4-inch lumber to frame the opening of your lattice door. You'll need a piece of framing lumber on either side of the door. Depending on the underpinning design, you may also need a piece at the top.
Insert the first piece of cut framing behind the lattice on one side of the opening. Drill pilot holes through the lattice into this piece of wood. Insert flat-head wood screws into these pilot holes and tighten to attach the frame to the lattice. Repeat on the other side of the opening, and at the top if necessary.
Cut four pieces of 1-inch-by-2-inch lumber to make a frame for your door. Attach the four pieces to the side of the inside of the piece of lattice you cut from the underpinning, with wood screws.
Attach one side of a set of hinges to the top and bottom of your door. Line the door up with the opening and attach the other side of the hinges to the door frame. Screw the hinges securely to the wood.
Attach a latch to the other side of your door.