Open Lattice Roof
An open lattice roof can be made by leaving space in between the beams. The amount of space depends on how much light you wish to come through to the porch. This choice gives you a lot of options, since you can place beams at any distance apart. You might choose to add decorative raft ends or allow the beams to be flush with the crossbeams.
Pergola Lattice Roof
Pergola is another type of wood lattice that gives you numerous design options for your lattice porch roof. Pergola can be used for the roof with matching beams on the sides. You can have many rafters so your porch is almost completely shaded or fewer so more sun comes through. Also, you could choose to use the Pergola so that the rafters go both horizontally and vertically across the roof. Depending how much light you want to come through, you can still space these very close together or farther apart. There are different kinds of rafter ends that can be used--some are extremely ornate and decorative, while others are of a simpler design.
Vinyl Lattice Roof
Vinyl lattice roofing is a good choice for certain climates, depending what style you want. Vinyl lattice gives you the option of color choices, while still allowing for the same type of sunlight to come through with the spacing of the beams. Vinyl lattice roofing is easier to maintain than wood, and it will not warp or fade over time. The vinyl lattice roofing can be matched to the color of the porch and any fencing around the porch as well.