I have to study this circuit. I understand that Graetz's bridge is there to convert the current to positive, but why is there a LC filter at the entrance of the converter?
why is there a LC filter at the entrance of the converter?
That looks like a noise removal filter. The noise is generated by the 12 volt switching converter (due to high speed switching) on the left and therefore, the LC immediately to its right (its input port) will act as a 2nd order low pass filter and noise/switching artefacts travelling from left to right (left being the input to the inductor) will be significantly attenuated. So, if the whole design needs to comply with some conducted emission testing (as measured at the far right on the 24 volt port), the LC provides assistance in meeting those requirements.
Note - it's quite common to see this circuit addition on many power converters such as "Traco" and "Exar" converter products. And, if you dig down into application notes for the TM 3-2412 (your device) you'll find this general recommendation: -