What is the 1k that shows up where LTE would be?
It's "1x" not "1k".

This is the core fallback 2G cellular connection of a CMDA (Verizon in the US) network. It's not showing up to replace your 4G LTE connection, it's your LTE that is failing and 1x is the only signal that can reach your phone.

The same thing happens with any carrier and it is by design. If you are in an area that is at the edge of their premium 4G service, you fallback to 3G then 2G. 

See Wikipedia page on CDMA for more details.