Low pass filter on PSU and target amplifier
Can we have a second LPF (LC) on the AMP ?


Yes, most class D amplifiers have both a low-pass filter between the power supply and the amplifier where the power goes into the amplifier, and also a low-pass output filter where the amplified output signal goes out.


  should we use a LC or PI filter ?


I recommend using exactly the filter recommended in the datasheets for the parts you are using, getting that working first, before experimenting with anything else.
For example, if you are using a MC56F series chip,
first tray to get it to work using exactly the filters recommended in
"LLC Resonant AC/DC Switched-Mode Power Supply using the MC56F8013 and MC56F8257".
For example, if you are using the ADAU1592,
first try to get it to work using exactly the filters recommended in the
"Applications Information" schematic shown on p. 21 of the ADAU1592 datasheet.
For example, if you are using the SSM2529,
first try to get it to work using exactly the filters recommended in the "Applications Information" schematic shown on p. 50 of the SSM2529 datasheet.


  cutoff frequency at 400Khz


That doesn't sound right.
Chi Ho Li,
"Design and analysis of a basic class D amplifier";
Würth Elektronik,
"Class D Amplifiers: Dimensioning and Calculating the Filter";
Richard Palmer,
"Design Considerations for Class-D Audio Power Amplifiers";
and
Bruno Putzeys,
"Switching Amplifier (Class D) Basics"
all imply that a class D audio amplifier typically has an output filter cutoff frequency around 40 kHz to 80 kHz.
(Is your system perhaps not typical in some way?)
Often the filter between the power supply and the class D amplifier
has a cutoff frequency well below 50 Hz.