Is a new token generated for the same user on different node on a load balancer with stickiness enabled?

My project (on angularJs) implementation is done in a way that a single webpage application is deployed on a load balancer with 2 nodes, I am not able to figure out a solution for the below problem.

Implementation:

• Each time a user logs in, a new token is created
• When the user switches to a different node (by any means), the user will need to login again on that particular node

Here is the scenario: (Note: The same User is logging-in from client1, client2 & client3)

Client1 -> lands and logs-in on node1 -> token1 is created
Client2 -> lands and logs-in on node2 -> token2 is created
    Now suppose node1 goes down (due to some reasons), 
Client3 -> lands on node2 by default -> Now,

Note: Since there is a token already generated on node2 for the user and the session here is active too, so

Questions

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1. Should the user be asked for login again on node2? OR
2. The user should be able to use the current/active session without login?
3. Why in either case?