Cellular yes, LTE no.
The reason the OP drops to no bars at all is that his carrier's non-LTE tower is too far away or its signal strength is so-so. When he is at home and not in LTE mode his signal sucks.
In my case, I have several AT&T towers surrounding my home. Sometimes I connect to one with a very strong, 4 or 5 bar signal, sometimes I connect to one with a weak 0 or 1 bar signal. And sometimes, if I disable Wi-Fi, I connect to an entirely different tower in LTE mode. I wrote about this a while back, here:
http://forums.androidcentral.com/google-nexus-5/332728-aio-t-tower-selection-algorithm.html
[edit to add]
Keep in mind, LTE is specifically a data connection and has nothing whatsoever to do with voice except in some brand new systems which are using VoLTE (Voice over LTE). That's why your phone drops its LTE connection whenever it has an alternate (read Wi-Fi) data connection.
http://en.wikipedia.org/wiki/LTE_(telecommunication)
http://en.wikipedia.org/wiki/VoLTE