AFAIK you can ensure a computer has a static LAN IP by just setting it like this:
-Double click the connection in Windows' Connections system folder.
-Click Properties.
-Select the TCP/IP protocol.
-Click properties.
-Type 192.168.0.136 in the first field.
-Type 255.255.255.0 in the second.
-Type 192.168.0.1 in the third.
-Set 192.168.0.1 as the DNS server.
-Click OK.
-Click OK.
-Click Close.

This is all assuming that your router has IP 192.168.0.1, which it should have by default afaik.