Can Honda cr-v 97 lx remote work for Honda cr-v 97ex?

Yes, the security systems SHOULD be compatible, if not identical.

Every CR-V has the receiver installed at the factory. There is nothing to install into vehicle. Simply program the remotes to your CR-V by turning the ignition on and off and pressing the lock/unlock buttons.

Regardless of what your dealer or anyone else tells you the CRV does not need anything installed for the keyless entry to work. The same module that handles the power door locks is the receiver for the keyless entry, if you have power door locks you have the receiver.