It seems that you will have a client (A) that will connect for example at 14H00. Another client (B) will send a message on the server for example at 3:00 p.m. What do you want to do and send an information in client A, to inform you that you have a new message.
It's impossible to be sure that this will work. Why?
1) between the client connection A at 14H00 and the moment you are going to send a 15h00 message, client A can change IP
2) If the client has 2 computers, a router and a modem, when the server will save the IP, it will not save the IP of the client, but the IP of the router. You can do the following test: put on your site a page that shows the IP, connects with a computer on your network and then another one on the same network and you will see that from the server's point of view the two have the even IP.
When we create a CHAT for example, it has the same problem: show client A, client messages B, C etc ...
The SignalR can be used, but not as you think. You say "How do I send a notification with SignalR to that particular client (based on login identity)?" which means that you think it's the server that's going to call client A.
Not possible (unfortunately)
Seriously with SignalR, you will determine the time of the call. And the A client that will (for example, every 5 seconds) call the server. Then the server will know who "calls" and will give the right answer.
You can take a look here:
link
You can also take a look here:
link
In the Scripts folder you have jquery.signalR-2.2.0-pre-140709-b104.js (lines 694 and following to understand the beginning).