What does "Lost Mode Pending" mean? In Find My iPhone, once setting the parameters to enable Lost Mode, the screen displays the status as Lost Mode Pending. 

Pending? Why is it pending?
Outside of the Lost Mode feature, I don't otherwise have a lock on my phone. 

How long will it be pending? Will the person with my phone be able to read my incoming texts while it continues to pend?
It will remain pending until it connects to the Internet. 

It is recommended to change your Apple ID and other affected passwords, although if connected to Internet, the device should enforce the Lost Mode and protect your content.

If the person who has your phone has prevented it to connect prior to you having set up the Lost Mode information present on your iPhone is visible to them until it connects.

It will be forever pending if it is put on recovery mode before being connected to Internet, but it won't be usable because of Activation Lock. In this case your data will be erased.