This is liturgical used as an adverb. It tells you how something is done: in the way of a church service, as part of the set worship. If a prayer is said liturgically, it is said in the service, with the usual words and order, not as a private talk with God. A meal can even be treated liturgically, with set words before and after. Same world as liturgical; this form just answers “in what way?” rather than “what kind?”. It is still a little formal, and you will mostly see it in writing about worship.