How to build LED dimmer for room illumination - PWM, low pass filter?
This is a good idea. Theoretically you could use the pwm as is to dim the lights since an LED shines brighter the longer the on-periods are. Your concern about sending waves might be negligible as long you stay in the lower kHz-domain, yet no blinking will be seen for the human eye. So first I suggest you to make a roughly 5kHz pwm signal and apply it to your LEDs. 

If you want to use a LowPass the calculation is easy:
f=1/(2*pisqrt(CL))
This describes the -3dB frequency. So if you apply any signal, frequencies above f will be attenuated by 3dB at f, and falling with 40dB/decade. 
Example: choose C and L for a frequency of 100Hz, then apply a signal, of 1000 Hz and it will be 40dB less than the original signal, means devided by thousand. A 10kHz signal will be have -80dB, means there is nothing left of the signal. 

So in your special case my suggestion is: make a 5kHz square signal from a controller and make an LC-LowPass for f=100 Hz (choose C e.g. 10 microF) and calculate L accordingly. 
It will produce perfect DC proportional to the pulsewidth. 

Only your cicuit layout is wrong and won't work. 







simulate this circuit &ndash; Schematic created using CircuitLab
Added: Diode D1 added. Inductor current cannot be interrupted. Current flows as per top arrow when Q2 is on and via D1 when Q2 is off.

I would try this, but I drew it quickly, so someone please look over it again!
Hope this helps