How to allow current over a certain voltage
If you want it to accurately switch you really need something more active like a comparator. This circuit will pull around 15mA through your LED when the voltage at the top of the LDR exceeds the voltage set by VR1. 







simulate this circuit &ndash; Schematic created using CircuitLab

There are other ways to do it with discrete parts, but seriously, you just end up with many more parts and a bigger circuit.