Jesper,
As a follow up:
There is nothing royalty free and up-front-fee fee free for the LH7A404 card engine except for Linux and LoLo (assuming that you are using card engine of course). Below is a link to Sharp's BlueStreak Software Library. This is where you would want to start if you were going to work with Linux on the A404.
http://www.sharpsma.com/mcu/mculibrary.php
The only OS that I can think of that is fairly simple and free is ECOS, but it has not been ported to any of our card engines except the SH7760.
http://sourceware.org/ecos/
Regards