I would suggest considering a motion sensor circuit such as low cost fully assembled module as used in burglar alarms (PIR).
However you asked about an LDR and the question is what is different between the change in ambient light level and someone walking past the detector?
Probably the rate of change in brightness, i.e. human movement is faster than the ambient light level.
But it's amazing how fast the ambient can change as clouds obstruct the sun, so this may not be true for a sensor that is sighted in an externally lit area.
Assuming a shaded indoor illuminated area, then an analogue differentiator to measure rate of change followed by a level sensing circuit may work.
What may upset this circuit is lights being switched on and off and indeed the person stopping in front of the LDR.
Added to this LDR's are relatively slow, probably faster than you need, but that has to be checked.
It's tending towards a beam break circuit where the LDR is in a tube to exclude stray light and a light source (probably a lamp) is focussed by a simple lens on to the sensor.
My feeling is that the simple LDR is not suited for simple motion detection when compared to the burglar alarm sensor which probably also has a relay output and an 'on' timer as used in external PIR light circuits.