Battery monitor shows charge again so that part is indeed solved.
However, it still doesn't give me any warning and I think I've got an idea why: there's an option to set the time to be left as the critical level, it's kinda hidden though as it doesn't show upon right-clicking the battery monitor itself and selecting
"Battery Monitor" Settings, you'll need to right-click anywhere on the panel and select
Add/Remove Panel Settings, find Battery Monitor in the list and click the Edit button (or double-click Battery Monitor in the list).
There you'll see the otherwise missing option
Alarm time (minutes left) which is set to 5 minutes by default.
When hovering the mouse pointer over the Battery Monitor a tooltip shows the remaining charge and time.
I'm willing to believe the remaining charge is accurate, however the remaining time always shows 0:00
A related problem has been posted to the LXDE bugtracker on Sourceforge as
Bug 3018792, on which I've commented.