Will the iPhone Lost Mode override disabled location tracking? We have an iPhone that has location services disabled since we've usually been able to find the device simply with the Find My Phone "Play Sound" function.

Unfortunately, we think the device might be hiding in one of our bags and thus we can't locate the phone by listening for the sound.

I've never used Lost Mode, but I have read ambiguous information that leads me to wonder: if I turn on Lost Mode for a phone, will it temporarily enable location tracking for the device so I can figure out where it is?
You should turn on lost mode. 

The next time it checks in over the network it will adjust location prefs and report in. 

If it never checks in, your last settings will prevail.