As reported in https://bitbucket.org/javafxports/android/issue/19/menu-button-not-mapped, the (hardware) menu button of Android devices is not mapped and and therefore not available in application code. The change in android.h in the following patch (which depends on the fix for RT-35130) is for the other vm on android. The dalvik port uses another file (dalvikUtils.h), where the same change must be applied.

diff -r d17f092867da -r 22f7e87e105b modules/graphics/src/main/native-glass/lens/LensInputEvents.c
--- a/modules/graphics/src/main/native-glass/lens/LensInputEvents.c Thu Dec 26 05:02:10 2013 +0100
+++ b/modules/graphics/src/main/native-glass/lens/LensInputEvents.c Sat Dec 28 04:28:42 2013 +0100
@@ -183,7 +183,7 @@
     {KEY_DELETE, com_sun_glass_events_KeyEvent_VK_DELETE, "", ""},
     {KEY_LEFTMETA, com_sun_glass_events_KeyEvent_VK_WINDOWS, "", ""},
     {KEY_RIGHTMETA, com_sun_glass_events_KeyEvent_VK_WINDOWS, "", ""},
- {KEY_COMPOSE, com_sun_glass_events_KeyEvent_VK_CONTEXT_MENU, "", ""},
+ {KEY_MENU, com_sun_glass_events_KeyEvent_VK_CONTEXT_MENU, "", ""},
 };
 
 static const unsigned int gKeyMapSize = sizeof(keyMap) / sizeof(LensKeyboardMap);
diff -r d17f092867da -r 22f7e87e105b modules/graphics/src/main/native-glass/lens/android/android.h
--- a/modules/graphics/src/main/native-glass/lens/android/android.h Thu Dec 26 05:02:10 2013 +0100
+++ b/modules/graphics/src/main/native-glass/lens/android/android.h Sat Dec 28 04:28:42 2013 +0100
@@ -178,6 +178,7 @@
     //{AKEYCODE_INSERT, KEY_INSERT},
     {AKEYCODE_DEL, KEY_BACKSPACE},
     {AKEYCODE_FORWARD_DEL, KEY_DELETE},
+ {AKEYCODE_MENU, KEY_MENU },
 };
 
 #endif /* ANDROID_H_ */