Currently I am using  using physical machine name (or VM name) to login to CIS studio. Based on my  institution security requirement, wanted to know whether I can login to CIS studio by using load balancer? what options are there for achieving this goal?

As per the Best Practices, it's not advised to login to active cluster via load balancer from studio because it might lead to discrepancy or inconsistency.

Whenever studio establish a session with server, it opens three connections and if any of the connection dropped then it's not certain which node it will connect Which might lead to discrepancy/inconsistency or sometime it might throw null pointer exception

However in non cluster Environment ,It   can be doable as long as configuring the same ports and IP address  on load balancer for the ports and IP  of  CIS is running .