No, Access needs the delete permission for the lock file...
You can explicitly set permissions on files as well... The caveat here is that everytime you do a compact/repair you are technically creating a new file with the same name in the folder so it will inherit the folder's permissions... or fail if you set the permission...
That being said, if you can manage the permissions yourself easily (or ask for them for the folder) you can twiddle it yourself.
Just do two things, discuss with an admin the possible fallout with compact/repair and why your want to remove ther permission... just in case you are not around.... and of course consider giving the delete permission back when you are not going to be around.
If you remove the delete permission, hopefully someone will ask why they can't delete the file... Which of course is another reason to tell the admin.