I am currently using GXT 3.0.1 and it does not support navigating the GRID outside the default grid view using the arrow keys. If we need to do so then you need to write a custom class as shown below.
Code:
     public class CustomLiveGridView extends LiveGridView {                 @Override                public void handleComponentEvent(Event ge) {                    if (ge.getKeyCode() == KeyCodes.KEY_DOWN || ge.getKeyCode() == KeyCodes.KEY_UP) {                    ge.stopPropagation();                           ge.preventDefault();                            if (ge.getKeyCode() == KeyCodes.KEY_DOWN ) {                                   liveScroller.setScrollTop(liveScroller.getScrollTop() + getCalculatedRowHeight());                           } else {                                   liveScroller.setScrollTop(liveScroller.getScrollTop() - getCalculatedRowHeight());                           }                           updateRows((int) Math.ceil((double) liveScroller.getScrollTop() / getCalculatedRowHeight()), false);                            syncScroll();                    } else {                              super.handleComponentEvent(ge);                    }    }