LTE Fallback with fixed public IP

I want to implement a LTE Fallback solution for our network, but the public IP should be the same as it is with our glass fibre network.
Is this general possible? I don’t understand if our fixed public IP will still be accessable through internet if i switch to the different (LTE Fallback) network. Can i configure that somehow in our Router or do i have to work with a second public IP? Thanks in advance.