This is speculation, but I think it holds up.
His Divine Shadow had two hidden but ultimate goals - the genocide of the human race, and the revival of the Insect Civilization. Lexx may have been designed for both.
First off, while the Foreshadow and the Megashadow are indeed quite capable of destroying a planet, they are also large flagships entirely crewed by humans. Whatever techniques the Divine Order uses to indoctrinate seem pretty effective, considering none of the humans seem to blink at blowing up planets, torturing, brainwashing, harvesting their fellow humans for parts/food, etc. Still, it might be best when trying to cleanse the universe of humanity to not rely on humans. Lexx was not only designed to eliminate a planet in a single shot, but to be run entirely by a single captain with the key. It was fairly obvious that captain was intended to be His Divine Shadow, so that he could run his genocide single-handedly if need be. (It is left for any given reader to judge whether Stanley is an improvement on that scenario, considering where the plot goes later).
Second, later in the first season we learn that there is a single surviving member of the Insect Civilization - the Gigashadow, who has been hibernating in the core of the Divine Order's home planet the entire time and pretty much cooked up the Divine Order to get things done while he hid. Since it takes up most of a planet himself, it can be presumed the Gigashadow has no problem smashing planets either, although as the last of his kind that would probably just make it a very large target. Since the Gigashadow is shown to produce offspring (which is brought up early in the 2nd season), it probably also has no issue repopulating the Insect Civilization itself. However, since the Lexx is also capable of producing offspring, from the smaller shuttle ships to the mini Lexx at the end of the series, it may also be that the Lexx was created to help the Gigashadow create more of itself.
All that said, His Divine Shadow certainly goes through some crazy and traumatic brain transfers as the series starts. None of his followers seem to be able to guess what the plan is either, and there's plenty of the Predecessor brains that question him too. So whether His Divine Shadow is actually any longer following the original plan for the Divine Order, or after all this time is just a few fries short of a happy meal and making half-baked mad plans that only kinda sorta fit the sleeping dreams of the Gigashadow, is an open question. The latter may actually better fit the chaos of the show.