The answer depends on your architecture and also your requirements. Do you need a loadbalancer for high availability? Or for performance reasons/scalability? Or both?
Elasticsearch like many other distributed systems comes with its own protocols and semantics to distribute load across multiple nodes and to manage fail-overs.
You can use these semantics to configure nodes in such a way that a node can perform just the role of a coordinator -- effectively acting as a load balancer for heavy duty operations like search requests or bulk index requests.
Elasticsearch also has its own built-in protocol for electing a new master node in case of failures -- again effectively performing the role of a load balancer.
In general, I would recommend you to use the native capabilities to achieve your goals instead of adding more complexity by introducing another technology in front of it.
If you want a stable URL for your cluster, then configure your DNS server to reach that goal. A cloud provider managed cluster should already have such a feature, otherwise you can configure it with some efforts.