If I get it right,You only need to convert the IP addresses at the moment that you intend to display them. So, you may store the numbers in 4 byte format (what about IPV6?). So theoretically there is no real limit.4 bytes with 256 addresses would generate 1K size array max.once you start to display it on an LCD, you can convert it send it to the display and use the same storage for the next IP address. Once it is transferred to the LCD, the variables used to generate the text version of the IP address can be reused again.
Since the addresses are contiguous you can use a bitmap to store a flag (present/not present) for each address. That will take up 32 bytes for a 256-entry bitmap.
Well, they might not be. I might be getting something like: