Surely a religion that claims godlessness and earthliness has no need for theistic rituals and invocations.
Who said anything about those being theistic rituals and invocations? LaVey's system of magic requires no belief in any external gods, devils, demons, spirits, etc. All experiences, if any, are subjective and even LaVey himself stated that even in his most powerful workings any personal manifestations are purely the externalization and visualization of his own ego and material/carnal desires.
"I have this awareness that the objectification is in accord with my own ego. I’m not deluding myself that I’m calling something that is disassociated or exteriorized from myself the godhead. This Force is not a controlling factor that I have no control over. The Satanic principle is that man willfully controls his destiny; if he doesn’t, some other man—a lot smarter than he is—will. Satan is, therefore, an extension of one’s psyche or volitional essence, so that that extension can sometimes converse and give directives through the self in a way that thinking of the self as a single unit cannot. In this way it does help to depict in an externalized way the Devil per se. The purpose is to have something of an idolatrous, objective nature to commune with. However, man has connection, contact, control. This notion of an exteriorized God-Satan is not new." Monologue from John Fritscher’s Popular Witchcraft by Anton Szandor LaVey (1973)
Also from the Church of Satan FAQ on rituals:
WHAT IS A SATANIC RITUAL?
Greater Magic, which is our name for our ritual practice, is basically meant as self-transformational psychodrama. That is it serves as a means to purge oneself of unwanted emotional baggage that might be hindering a daily pursuit of joy in life. We do not require that anyone accept that it is more than this. The pageantry of ritual is a drama meant for emotional stimulation, not a belief in or worship of any power higher than the projected will of the magician. That is why we call it an “intellectual decompression chamber.”
The three basic types of Satanic Ritual are outlined in detail in The Satanic Bible, which is essential reading for those wanting to grasp our perspective on this practice. They are for Compassion (for oneself and others), Lust (to release unrequited sexual urges) and Destruction (to cleanse oneself of anger towards someone who has done you an injustice). These serve as models for whatever other purposes one might feel the need to explore via ritual. In The Satanic Rituals Anton LaVey presents other rituals essentially meant for larger group performance based on historical and cultural diabolist imagery.
However, some Satanists also consider the possibility that, through the raising of emotions focused towards a specific achievable goal in ritual, ideas/concepts/images might be transmitted to the minds of other people at a distance, thus perhaps influencing them to make future decisions favorable to the outcome of the situation desired by the magician (transmitter). It then seems to us plausible that there would be a means that is part of nature through which this works. It is not attained through the intervention of supernatural beings, as we do not believe such things exist. The desired goal, what we call an “Is-To-Be”, would vary based on peoples' ability to transmit as well as receive such images as well as the likelihood of the situation towards which the magician is working.
Rupert Sheldrake, a biologist, has spent many years exploring the “extended mind” and has solid statistical evidence that there indeed does exist a mechanism in nature that could be used for such ends. His many books are fascinating and worth investigating.
We emphasize that the philosophy of the Church of Satan does not require that our members believe that ritual is more than an emotional experience, nor is there a mandate even to ritualize at all. We simply offer it as a tool for experimentation. Some folks have found results that they feel are beyond coincidence or statistical parameters. Others simply enjoy the release of emotions otherwise hindering their pursuit of personal happiness.
There is no judgment placed on members of the Church of Satan regarding their personal understanding of how ritual functions. One is not more or less of a Satanist based upon his or her evaluation of Greater Magic. See the essay, “On the Role of Ritual in the Life of a Satanist” by our High Priestess, Magistra Peggy Nadramia, for more information.