Does switching my phone from 3G to LTE only matter if I use mobile data?
If you keep your mobile data off, it rather depends on coverage:


Good 2G coverage? Use that. Your battery will last much longer.
Shaky 2G but stable 3G? Use 3G. Same reason: shaky coverage makes the phone permanently switch cell towers, which eats your battery.
2g &amp; 3G shaky, but stable LTE? Well, you guess it.


For a more detailed answer backed by "hard data", see 2G versus 3G: Does it really save battery? Doesn't mention LTE, but you can "extrapolate". Apart from that, with LTE in an early implementation, yur device would need to switch to 3G anyway for phone calls (that was only fixed later).