Chromevox has a shortcut that allows a user to pass the next key through to the OS. I think that this is the only way to deal with this problem. There are simply not enough modifiers on Chromebooks to reserve a key only for Chromevox.

This issue has been Available for over a year. If it's no longer important or seems unlikely to be fixed, please consider closing it out. If it is important, please re-triage the issue.

Sorry for the inconvenience if the bug really should have been left as Available.

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Google Chrome	70.0.3524.2 (Official Build) dev (64-bit)
Firmware Version	Google_Lulu.6301.136.57
 
Testing ChromeVox with each of these areas:

lock screen, search + l: fail, conflicts with next list
suspend, shift + search + l: fail, conflicts with previous list

caps lock, alt + search: pass, works   
page up/down, home, end: Alt + Up arrow, Alt + Up arrow, ctrl + alt + up arrow, ctrl + alt + down arrow: pass, no conflict in that they still work with ChromeVox on; however, it doesn't actually advance the ChromeVox focus which is another bug 877564
task manager: search + esc: pass, opens (master bug for task manager is bug 101762)
delete: delete next character is alt + backspace and delete previous word is ctrl + backspace: works but ChromeVox doesn't announce it, bug 877572
context menu: shift + search + volume up: pass, works 

Since most of these conflicts are now fixed, I'm going to open another bug just to isolate the two that still fail: 
lock screen, search + l: fail, conflicts with next list
suspend, shift + search + l: fail, conflicts with previous list