Cannot communicate on LAN when WIFI doesnt have internet This is pertaining to a smart phone with data. 

My phone is connected to my WIFI which lacks internet currently. It is also connected to the cell network and using it for data. When I ifconfig it tells me I am connected on wlan with 192.168.1.4 and rmnet at 10.124.121.12. I am trying to ping a device on 192.168.1.55 for purposes.

If I turn off my cell network I can ping it fine. With my cell network on its unreachable. 

How do I get my android to allow me to ping 192.168.1.55 while being on the cell network? I have only noticed this since the internet went out on my WIFI so its a strange and new problem.
you cannot ping that device via Mobile Data.
You have Device 1 (yours) and Device 2 (device to be pinged).
Telling from the IPs given, both devices are on the same WiFi network. Device 1 can connect to Device 2 by requesting a ping to Device 2 on your router (Device 3).

Your router is most likely having the IP 192.168.1.1

As your router knows that you are connected to it, it will forward your ping request to Device 2 and back again.

When connected to your mobile carrier, you have a different IP. But, your router uses IPs to determine whether it knows a device or not. As you have a different IP and your ping request comes from the outside now, it does it's job: Not forwarding your ping requests. That's what the router is there for (besides establishing connections). It is a firewall and it's trying to prevent people from outside harming your devices.

When you are connected to WiFi


When you are connected to Mobile Service Data Provider


This means, that you are not actually having an Android Problem. What you need to do is to tell your router to forward PING packets. That's difficult. For that, you should head over to the Servers Fault community and ask them how you can do exactly that.

https://serverfault.com/