If you already have a LAMP + WordPress installed in your local machine, you can access your application by using the private IP of that Linux computer. You can run this command to obtain it
Once you have the private IP, you will need to use the port that Apache is using, in this case the 8080 one.
It's possible to use the domain name if you configure the different devices to resolve the domain you want to use to the private IP of the machine but you will always need to use the port when accessing it.
Note that all the changes you make when using WordPress will be available in all the devices you use when accessing it. The information is stored in the Linux machine you have with LAMP and WordPress and you won't need to enable a plugin for the different devices you have.