WordPress by default is hardcoded to a single URL, so you will not be able to access WordPress from two different raw IP addresses. Beyond that, the Raspberry Pi forums are a much better place to ask your questions:
https://www.raspberrypi.org/forums/
It can be done, several variations as to how.
Dione is correct in that you only have one setting for the site address and WordPress address in your WP settings, but it can mean different things to different computers depending upon where they are and how they are configured.
Configure your RaPi to have a fixed IP address on your LAN.
A) You have a permanently assigned and fixed IP address for your internet gateway.
Get a domain name or subdomain, set the nameservers to point to the router’s permanent IP address, set port forwarding to your RAPi, configure the WordPress to use the domain name in the site address and WordPress address. Configure the Apache server to use the “virtualhost” method, details here:
http://httpd.apache.org/docs/current/vhosts/name-based.html
B) You don’t have a permanently assigned IP address from your ISP, so use one of the dynamic IP solutions, otherwise similar to A) with a name that uses the dynamic IP service.
On your LAN, use the “hosts” file on each computer to map to the RaPi, including the RaPi’s “/etc/hosts” file itself, details on hosts files here: https://en.wikipedia.org/wiki/Hosts_(file)
Now computers on the LAN, and on the internet, all can see your RaPi server.
On the other hand, if your ISP has given you a permanently assigned IP, then ignore the virtualhost method, set the WP site address and WordPress address to this, maybe the router will still redirect LAN traffic using the port forwarding, even when the traffic comes from the LAN side.
