What happens if capacitor and inductor connected in parallel with led?

Without knowing the signals driving such a circuit and the tuning of the tank in the circuit it in not possible to give an exact answer. However assuming the tank is tuned to RF the behavior of the tank and LED should be effectively independent: the tank will respond to the RF in the signal and the LED will respond to the DC in the signal. The behavior would be different if the tank was tuned to low audio frequencies.