[roman]

El comportamiento que mencionas es raro porque, usualmente, el directorio de la aplicación tiene prioridad sobre cualquier otro directorio.

Como alternativa, lo único que se me ocurre es que coloques esta unidad en tu aplicación (pones la ruta adecuada en SQLite3DllLocation):

Código Delphi [-]
unit SqliteLoader;

interface

implementation

uses ZPlainSqlite3, ZPlainLoader;

const
  SQLite3DllLocation = 'c:\ruta\a\la\biblioteca\sqlite3.dll';

type
  {** Implements a loader for SQLite native library. }
  TZSQLiteNativeLibraryLoader = class(TZNativeLibraryLoader)
  public
    function Load: Boolean; override;
  end;

{ TZSQLiteNativeLibraryLoader }

function TZSQLiteNativeLibraryLoader.Load: Boolean;
begin
  Result := inherited Load;

{!}        @sqlite_open                   := GetAddress('sqlite3_open');
{!}        @sqlite_close                  := GetAddress('sqlite3_close');
{!}        @sqlite_column_count           := GetAddress('sqlite3_column_count');
{!}        @sqlite_column_bytes           := GetAddress('sqlite3_column_text');
{!}        @sqlite_column_name            := GetAddress('sqlite3_column_name');
{!}        @sqlite_column_decltype        := GetAddress('sqlite3_column_decltype');
{!}        @sqlite_exec                   := GetAddress('sqlite3_exec');
{!}        @sqlite_last_insert_rowid      := GetAddress('sqlite3_last_insert_rowid');
{!}        @sqlite_changes                := GetAddress('sqlite3_changes');
{!}        @sqlite_errmsg                 := GetAddress('sqlite3_errmsg');
{ ?-       @sqlite_last_statement_changes := GetAddress('sqlite3_last_statement_changes');}
{!}        @sqlite_interrupt              := GetAddress('sqlite3_interrupt');
{!}        @sqlite_complete               := GetAddress('sqlite3_complete');
{!}        @sqlite_busy_handler           := GetAddress('sqlite3_busy_handler');
{!}        @sqlite_busy_timeout           := GetAddress('sqlite3_busy_timeout');
{!}        @sqlite_get_table              := GetAddress('sqlite3_get_table');
{!}        @sqlite_free_table             := GetAddress('sqlite3_free_table');
{!}        @sqlite_freemem                := GetAddress('sqlite3_free');
{!}        @sqlite_libversion             := GetAddress('sqlite3_libversion');
{ ?-       @sqlite_libencoding            := GetAddress('sqlite3_libencoding');
{ ?-       @sqlite_create_function        := GetAddress('sqlite3_create_function');}
{ ?-       @sqlite_create_aggregate       := GetAddress('sqlite3_create_collation');}
{ ?-       @sqlite_function_type          := GetAddress('sqlite3_function_type');
{!}        @sqlite_set_result_string      := GetAddress('sqlite3_result_string');
{!}        @sqlite_set_result_int         := GetAddress('sqlite3_result_int');
{!}        @sqlite_set_result_double      := GetAddress('sqlite3_result_double');
{!}        @sqlite_set_result_error       := GetAddress('sqlite3_result_error');
{!}        @sqlite_user_data              := GetAddress('sqlite3_user_data');
{!}        @sqlite_aggregate_context      := GetAddress('sqlite3_aggregate_context');
{!}        @sqlite_aggregate_count        := GetAddress('sqlite3_aggregate_count');
{!}        @sqlite_set_authorizer         := GetAddress('sqlite3_set_authorizer');
{!}        @sqlite_trace                  := GetAddress('sqlite3_trace');
{!}        @sqlite_compile                := GetAddress('sqlite3_prepare');
{!}        @sqlite_step                   := GetAddress('sqlite3_step');
{!}        @sqlite_finalize               := GetAddress('sqlite3_finalize');
{!}        @sqlite_reset                  := GetAddress('sqlite3_reset');
{ ?-       @sqlite_bind                   := GetAddress('sqlite3_bind');}
{!}        @sqlite_progress_handler       := GetAddress('sqlite3_progress_handler');
{!}        @sqlite_commit_hook            := GetAddress('sqlite3_commit_hook');
{ ?-       @sqlite_open_encrypted         := GetAddress('sqlite3_open_encrypted');}
{!}        @sqlite_rekey                  := GetAddress('sqlite3_rekey');
{!}        @sqlite_key                    := GetAddress('sqlite3_key');
end;

initialization
  if Assigned(ZPlainSqlite3.LibraryLoader) then
    ZPlainSqlite3.LibraryLoader.Free;

  ZPlainSqlite3.LibraryLoader :=
    TZSQLiteNativeLibraryLoader.Create([SQLite3DllLocation]);
end.

Básicamente, esta unidad "copia" lo que hace la unidad ZPlainSqlite3 que es donde se carga la biblioteca de sqlite.

// Saludos