Would it mean any difference for a desert, where the amount of threatened objects is so low? Or would it form the geology and in general, the scenery somehow?
Apart from the, already mention in comments, creation of fulgurite the lightning discharge also produces a very strong magnetic field that is believed to be the origin of lodestones (a naturally magnetized magnetite). Magnetite itself is typically found in beach sand (mostly likely transported trough erosion).
A lodestone can attract iron and - I speculate - could in time, given an extreme frequency of lightning strikes, lead to abnormal concentration of iron (perhaps darker patches on the floor surrounded by a sandy color?). This is not totally unheard as can be seen by the existence of desert varnish (although mind the origin).
Lightning also oxidizes nitrogen in the air making nitrates which may lead to conditions more favorable to plant growth. It's a possibility that given enough time this hypothetical desert would became less barren although I do not have an opinion about what kind of plant life (inc. fungi).
As an unrelated note on Lightning (but perhaps useful for people who wish to further explore lightning related phenomena in world building) check this.