computing the parity of diagnostic requests' frame id
In LIN, whichever frame identifier (that is 6 bits long) the master sends is subject to parity computation, or-ing P0 and P1 as bits 6 and 7, respectively.
Examples:

0x3C is sent unaltered (P0 = 0, P1 = 0).

0x3D is sent as 0x7D (P0 = 1, P1 = 0).


My initial doubt was these values (used for diagnostic messages) were treated in a special way, but that is not the case.