Put on your gardening gloves. The leaves contain a whitish sap that will leak onto your skin while you remove the plant from the ground. While it is not poisonous, it can cause an allergic reaction.
Dig around and under the base of the plant with the trowel. The entire root system needs to be removed, which can be up to 6 inches deep. Once the entire root system of the wall lettuce has been exposed, grasp the plant by its base and pull it out of the ground.
Discard the plant in a yard waste trash bag. Since this is an invasive species, do not compost the plant because composting can spread the seeds around your yard.
Prepare the glyphosate weed killer according to the instructions on the bottle. Spray it into the area formerly occupied by the roots of the wall lettuce to kill roots that you missed. Refill the hole with topsoil.