Figured it out:
<applet code="org.lwjgl.util.applet.AppletLoader" archive="lwjgl_util_applet.jar" codebase="." width="640" height="480">
needs to be
<applet code="org.lwjgl.util.applet.AppletLoader" archive="lwjgl_util_applet.jar, lzma.jar" codebase="." width="640" height="480">