Has anyone created a analogue LEGO clock that runs time accurately?
Building a clock is easy, building an accurate clock is hard, even without lego.

To have accuracy you must have something happening at a fixed frequency.
A pendulum is the easiest way to provide a regular timing.

Next you need a power source for the clock.
Weights falling down is classic, and easy to do with lego : a pulley and a string.

The force generated by a spring is not constant, it decrease with time as the spring wound down. You need a constant force to have accuracy.
Real clocks have mechanisms to compensate this variations by I am not sure it is possible to replicate with lego.

An electric motor is better, but the charge of the batteries determine the power generated by the motor.

Then you will loose power with friction so you must limit the number of moving part or limit friction with lubricant for example. 

I have built a clock myself, it works but stops after 15 to 20 minutes for too much friction.
You can search the web for other lego clocks, but the best I have seen works for about 6 hours.

A lego clock is a fun project but you won't use it to tell time.