What is meant by 'local' in local oscillator?

You got that wrong: The "local" in oscillator doesn't describe the kind of oscillator used. It could just be an LC-tank, it could be a crystal-derived oscillator, it could be something synthesized from a reference clock or something recovered from the data stream received:

The "local" in oscillator refers to the fact that it's what the mixer uses locally to mix down or up, as opposed to the oscillator at the other end of the communication, which simply isn't the same oscillator.

Think of frequencies. The local oscillator generates a local frequency, that is only used by your mixer as the intermediate frequency. Whereas the transmitter frequency is not staying on your local board but flying through the air as radio waves. The transmitter and the receiver does not need to use the same intermediate frequency, but could use different local oscillators.

LO to an RF Engineer means a "local" sine wave signal or "within the device" (or Radio) used for heterodyning or RF mixing.

^{simulate this circuit – Schematic created using CircuitLab}

The LO could be fixed or a synth or a VCO with PLL to tune RF to the fixed IF filter. It may be used as an up- or down-converter.