A small LDR is approx 10K when illuminated and 1M when dark. This varies at least +/-1 decade depending on size and ambient light.
YOu can invert in many ways. Use a pullup R with LDR on input to ground or visa versa.
You can drive the LED ANode high or drive the Cathode low with Anode to V+ (eg 5V)
The LDR will need some backlash to prevent flickering thresholds. A Schmitt trigger gate will do this easily for a wide dynamic range LDR. A 50% backlash on the gate is large but the dynamic range of the LDR is large 100K to 1M for dark for example.
Since the LDR and ambient dark threshold are both undefined in your specification, you must use something like a 1~10M pot in series perhaps with a fixed R of 100k pot to define the "dark" threshold voltage where the gate changes from one state from 0 to 1 or a 1 to a 0 depending on above choice.
The CMOS inverter gate comes in hundreds of varieties for you to choose. Some can drive only a mA, others more. Usually the internal resistance of the CMOS gate depends on Vcc and part number( RdsOn is around 100~1000 Ohms, but is not stated in CMOS spec) so current limiting is built in.
The ESR series resistance of the CMOS Schmitt Inverter but depends on supply voltage.
THe LED resistance (ESR) varies with current from 1k ( dim ) to 15 Ohms bright for a 5mm part.
Obviously if the LED light shines on the LDR, it will affect the output, oscillate and not go on full bright.