After a few weeks of back and forth with Dell support, an on-site service was arranged to replace the motherboard. But even with the new motherboard, the lid crash problem persisted. So a second on-site service was arranged to replace the lid/LCD assembly and keyboard/top case, and so far it seems to have fixed it. Must have been something to do with the sleep/wake sensor, wherever that is on the Inspiron 5391. I was lucky that the laptop had 4 years of Premium Support. Fingers crossed that the issue doesn't resurface. 
Its specs are: When its lid is opened after having been closed (regardless of what the lid settings are), it'll appear to wake from sleep/hibernate, displaying the Dell logo and the spinning dots, but once logged in, all previously opened apps/programs will have closed. Opening the web browser will ask to "Restore pages" due to it closing unexpectedly. Sometimes it'll even wake straight to the "It looks like Windows didn't load correctly" screen, with buttons for "repair options" and "restart my pc". To investigate this issue I've used /sleepstudy to try to pinpoint the issue. Based on this sleepstudy report, it appears that the laptop crashes just prior to (or at the moment of) booting back up from the lid opening. But because the laptop is configured by default in the BIOS to boot up from a cold boot when the lid is opened, I believe it actually crashes when or after the lid is closed. The crash shows up as an "Abnormal shutdown", but no entry reason is listed. I think it shows up in Event Viewer as a critical event "Kernel-Power" with ID 41. [IMAGE] However, if the laptop is put to sleep without closing the lid (through the start menu or by pressing the power button), it'll reliably wake from sleep/hibernate, but only if the lid isn’t closed at any point after the fact. [IMAGE] The only workaround I've found was to manually hibernate the laptop first, then once it's in the hibernate power state, the lid can then be closed without losing any work. Next time the lid is opened, sometimes the power button will need to be pressed before the laptop will wake from hibernate.  Things I've tried, but were unsuccessful at fixing this issue: Things I've not tried: I am fairly confident that this is either a BIOS or hardware issue, since it occurs even in Ubuntu and persists across multiple Windows installs. Is there anything else that I can try, short of sending the laptop away?
Inspiron 13 5391 almost guaranteed to crash if lid is closed, losing 
work/progess/open apps