Is there a way to allow a certain app to work on LAN?

So I have a fairly specific question here and I've tried googling various variations of the question with no luck. Basically the scenario I have is that I will be helping to run a camp this summer, and it would be very nice to have our staff team be able to communicate by text (preferably through GroupMe or a similar group chat app). However, the camp is out of cell service for most providers and there is no internet available. However, there is a camp LAN network. I was wondering if anyone knew of a way to enable local communication on a smartphone app across the network? We don't need to be able to communicate to the outside world so we don't need an internet connection, but I would like to be able to use the features of a smartphone text app to communicate with others on the network.
I realize that my hope in a solution for this problem is fairly low but I thought I might as well ask. Thanks all for your help!