Yeah, turn it off, as searching for LTE constantly uses battery.
But, every so often, you might want to turn it back on for a few minutes or so to check and see if they've lit it up in your area. Where I live, AT&T does not have LTE on the map, but they recently turned it on just a couple weeks ago, and it works. So, it makes sense to check now and then.
And FYI, battery life is fine with LTE locked in and working.