We don’t recommend lining a wooden planter. Moisture will get trapped between the lining and the timber and cause wood rot to set in.
Also, if a plastic lining is used, its leaching chemical components might be an issue of concern for an organic gardener.
There is, however, an exception. If you use a planter treated chemically or made from pallets and grow edibles, the inside should be lined with food-grade plastic to reduce the risk of chemicals leaching into the soil and the plants.