TLS with load balancer and Web server
This depends on how the load balancer is configured.
In my experience load balancers are often configured to do TLS offloading. This means that TLS is stripped at the load balancer and the communication from the load balancer to the web server is over HTTP (and not over HTTPS). In this scenario, you web server is not even running accepting HTTP traffic over TLS.
If the above scenario does not apply, all TLS versions should be similar. This means that both should be configured to support TLSv1.2 or better.