Have some church

The expression "let's have some (something)" is colloquial, and often used to initiate an activity with a group. In Google Ngram, "let's have some fun" makes up a significant percentage of the results for "let's have some." It'd also be possible to use other objects, like food, drink, or a specific state like quiet:

Let's have some dinner, Dad. (The Quest for the All-Seeing Eye)

Okay, Fenfang, let's have some beer. (Twenty Fragments of a Ravenous Youth: A Novel)

"Let's talk for a little while and then let's have some quiet time" (The Working Parents Handbook)

Let's have some church fits the same pattern. It feels colloquial because "some church" is an unusual collocation, but within the larger pattern it makes sense. Absent context, it would mean initiating a church service, or more colloquially the music or gravitas a church service brings.