Shift-Reloading the lwjgl demo applet page causes firefox (3.5.3) to consistently crash on Mac OSX 10.5.8. Also, if you have multiple tabs up, the gears applet will show over the top of every tab. Safari 4 does not seem to exhibit either behavior.
The tab glitch is really a problem with the way firefox does tabs and not really something lwjgl developers can change/fix (happens with jogl applets too).
As for the crashes this is a rather serious issue, the main problem is that mac applets are still pretty unstable as they use the java plugin1, once they move over to the new java plugin2, the crashing issues should be resolved. As you will be able to run each applet in its own separate vm.
Hmm, but doesn't Safari use the same plugin? Reloading appears to work fine there.
I'm assuming your using java 1.5?
also can you try a few other lwjgl applets to see if they work? incase the lwjgl demo applet is broken
example 1 (http://gamejolt.com/online/games/shooter/final-kapster/693/)
and
example 2 (http://www.minecraft.net/)
I think Firefox uses the 3rd party Java Embedding Plugin
(http://javaplugin.sourceforge.net/Readme.html)
while Safari uses Apple's proprietary plugin interface.
The author of the plugin writes "The Java Embedding Plugin is a beta app that heavily depends on undocumented APIs. So there will be problems, and I need your help to fix them." and so perhaps this is one of those cases.