Is there a hot key to close all take lanes in X3?  
Often I have the several take lanes active on multiple tracks and want to minimize all, however the corresponding tracks are often minimized enough to not show the Take Lanes on/off button.   I would like a quicker method of closing them without having to first expand each track just to get to the button that allows me to minimize the take lanes.

SHIFT-T will expand or collapse the take lanes in the current track

Note that Shift+T isn't exactly the same as clicking the Expand/Collapse Take Lanes button. If you have Auto Track Zoom enabled and switch between tracks with their lanes expanded you'll see the difference in behavior (I think it's a bug). Also, there's no shortcut key to expand/collapse take/automation lanes of ALL tracks at once (which I requested via FR recently).

+1 on the request

try quick grouping.
Select all tracks (ctrl+a), and hold ctrl while pressing the takelane button on one track

Does it work? I think I tried it already.

I'm not at my DAW  now, so I'm not sure. Just a suggestion