Bit order for generaic std_logic_vector with dynamic width

You can provide a deterministic descending range with an object alias:

library ieee;

use ieee.std_logic_1164.all;
entity lfsr is
    generic (
        INIT:  std_logic_vector
    );
    -- In the entity declarative part:
    alias DINIT: std_logic_vector(INIT'LENGTH - 1 downto 0)  is INIT; 
end entity lfsr;

Use DINIT in the architecture where you'd have previously used INIT.

You could alias INIT in the architecture block declarative part or any declarative region (e.g. process statement, block statement, generic_statement, subprogram definition) in the architecture within the scope of the generic declaration:

library ieee;

use ieee.std_logic_1164.all;
entity lfsr is
    generic (
        INIT:  std_logic_vector
    );
end entity lfsr;

architecture foo of lfsr is
    alias DINIT: std_logic_vector(INIT'LENGTH - 1 downto 0)  is INIT;
begin
end architecture;