As far as I know from reading a few books on the topic: the concept of a "movie theater" didn't exist when the Lumière brothers organised the first screening in Paris. They rented a "Salon" (Salon du Grand Café), where they ran the screenings for a few days or weeks.
In the following years, their "business model" consisted in sending a dozen of trained operators across the world, to produce film sequenced and show them to the public. Those "Opérateurs Lumière" arrived in a city, rented a theatre hall and ran their show for a few days or weeks, before moving to the next city. At that point, the Lumière Camera wasn't available yet for purchase, they kept their technology a secret. An important fact is that the Cinématographe had two operating modes, it was both a camera and a projector. It was a very portable solution allowing to run projections on the go (provided that electricity was available).
This "world tour" program, which lasted a couple of years, was a publicity effort by Lumière to make their new invention known internationally. In a second phase, they made their camera (Cinématographe Lumière) commercially available. Their core business was the production of photographic film.
I hope this answers your question! Sorry for the delayed response.
Best,
Manuel