Why An LC oscillator sets its frequency with a resonant tank circuit, a coil and capacitor whose resonant frequency is f = 1 / (2*pi*sqrt(LC)). The amplifier stage supplies gain and feedback in phase, but the tank decides which frequency survives, because that is where the circuit's impedance peaks and losses are lowest. Change either the inductance or the capacitance and the output frequency moves.
Watch out Counters and dividers belong to digital frequency synthesis, where a fixed reference is divided down, not to a free-running LC oscillator; time delay in a lag circuit describes an RC phase-shift or multivibrator type of oscillator.
LC oscillator = L and C. Frequency lives in the tank: f = 1/(2*pi*sqrt(LC)).