First, thanks to everyone for your responses.
personally wouldn't recommend you use such an old version of LWJGL especially for applets, I'm surprised it still works 
Yes, indeed. I'm always happy if our applet works

I tried once to do that, but unfortunately there is an old JMonkey-Engine
http://www.jmonkeyengine.com/on top of an old LWJGL.
JMonkey has experienced lots of API changes, so updating JMonkey and
LWJGL is not an easy task for me and unfortunately I didn't write the applet
that I have to maintain now.
But someday I hope I am able to upgrade to the greatest LWJGL and Jmonkey,
then I will sit down, look back and I will put on a big smile

Sealed : false must be more friendly
Thanks, I have removed [Sealed: false] from my make-file.
Didn't change anything, though.
So make sure *everything* is signed by the same certificate - and has Trusted-Library: true
Everything is signed with the same valid certificate and has Trusted-Library: true.
<applet archive="myMain.jar, jme.jar, lwjgl.jar, windows_natives.jar">
I have checked all jars with jarsigner -verify, everything's correct. The manifests are there, too.
The browser shows my certificate, when starting the applet.
There was one thing that seemed strange to me. When I removed windows_natives.jar
from my applet tag, leaving
<applet archive="myMain.jar,jme.jar,lwjgl.jar">
it still works (even after deleting the java cache manually).
Having a look into the source-code in (org.lwjgl.util.applet.)LWJGLInstaller.tempInstall
I saw that windows_natives.jar was hardcoded there. It loads the file and copies
it into my temp directory. So this is where the "mixed code" comes from, is that so?
private static final String NATIVES_PLATFORM_JAR = "/" + LWJGLUtil.getPlatformName() + "_natives.jar";
InputStream is = LWJGLInstaller.class.getResourceAsStream(NATIVES_PLATFORM_JAR);
File tmp_jar_file = File.createTempFile("lwjgl", ".jar");
copyFile(is, new FileOutputStream(tmp_jar_file));
And being loaded "secretly", the Java VM can't have a look at the manifest files
to avoid the "Mixed code" warning in the browser ?
Thanks