Yes, new subscription requests have to be issued, as the LSClient object does not keep the state of the subscriptions:
it just forwards application requests for connections and subscriptions and only takes care of managing rebind requests autonomously.
On the other hand, the LSProxy object, available in the same interface, provides a broader abstraction and takes care of keeping the requested items subscribed across disconnections and reconnections.
This, however, requires some conditions and involves taking a lot of recovery decisions that may reduce the autonomy of custom code
(see the docs for details).
