At first it of course depends on the verification mode and there are a few different currently.
The second thing is: No it does not really have to be the same IP. I just told it because it was the easiest solution/use case I could see.
Generally (when using a non-DNS-based verification method) you just have to get the traffic from the LE server to your Raspi which you want to verify. So It's all about this step:
How you do this is your thing. BGB routing can be manipulated quite easily, but... eh.. no that's more an attackers scenario. 
Other things you could do include temporarily changing the DNS record or just using another challenge method like DNS-based verification.
So you see: It depends...