The Lamp sits apart from the elemental weapons and is easy to misfile beside them. The four implements, Wand, Cup, Dagger and Pentacle, each carry one element and each attach to one grade. The Lamp carries none of the four. It is assigned to Spirit, the fifth term that the Western scheme adds above the elements, and it does not belong to a grade in the same way.
Its ancestry is in the grimoires rather than in the grade system. The Key of Solomon and its relatives require a light in the working place and give instructions for it, and there the lamp is a practical necessity that has acquired a meaning, which is the usual direction of travel for ritual objects. What it came to mean is constant across the later literature: the light that is not the magician's own, whether that is named as divine, as the higher self, or as the Holy Guardian Angel in the vocabulary Crowley made standard.
Two things follow. Because the Lamp represents what is received rather than what is wielded, it is generally the one implement not consecrated to the operator's will, and several treatments say so explicitly. And because it is a light rather than a tool, it is the implement present throughout a working rather than taken up for a part of it. A list of four elemental weapons that adds the Lamp as a fifth is not wrong so much as flattening a difference the sources keep.