Assume that, there is a LC circuit without dissipation element R, implies that the power supply is always equal to the rate of stored energy. Can we consider this system as passive system?
An active systems is a system that can (in a particular mode) generate electrical power. Example a motor that is driven by its shaft/wheels of a vehicle (generative braking)
Lets start form definition of Active and Passive systems
The Active systems require external source of Energy to manipulate the input(s). on the other hand, the Passive systems process the Input(s) independent of external source of energy.
But we need to define the meaning for "External". imagine you designed a Filter using a set of Op-Amps. the circuit uses embedded battery. the question is " Is the battery an external source of power while it is embedded in the circuit?" the answer is YES and you filter is an ACTIVE Filter.
Form this standing point of view, your RC network is Passive, regardless of its ability to store energy. It generate its output by dissipation of kinetic energy of moving electrons and storage of energy in electrical field within the Capacitor metallic blades.
Let us assume that we have power source suppling an ideal capacitor and inductor (without parasitic elements). After short circuited the input terminal the energy may leads to oscillate between the capacitor and inductor circuit. The kinetic energy of the inductor (magnetic energy) charging the potential energy of the capacitor (electrical energy) and get discharged again into kinetic energy. Can we exactly say that this system is passive? since the enrgy not dissipated
The definition of Passive and Active systems are not related to Dissipation of energy, as I know. It is mostly related on the boundary of your system ( and in some systems the source of information).
as you mentioned above, the source of energy is internal within your system. the result is some sort of oscillation. there are some question about your loss-less assumption:
the existence of energy-dissipation is not a matter of interest, but it worth to note that your inductor and capacitor starts to radiate electromagnetic fields through capacitor's fringing fields and inductor's associated oscillating magnetic fields. so it will dissipate energy by filling the surrounding environment with EM fields. you can reduce it but can not eliminate.
How do you know the system starts to oscillate? do you measure? is there any indication system, i.e. an LED? Adding any measurement probe or ant indication system act as an output to your system which reduces the amount of energy of your system. so it starts to damp. if you need it to continue to oscillate, you need an external source of energy.
imagine an impossible situation: we know the system is oscillating without the requirement of (2). and the system will not radiate its stored electrical energy in thermal and electromagnetic forms. it is an stand-alone system, just converting some sort of energy to some other. the overall system is not Active because it is not using an external source of energy, beyond its boundaries. Closed systems are considered as passive systems; as they are not interacting with environment out of their boundaries.