My understanding is that doesn't apply to LTE, right?
Actually, it does if the problem is inability to operate on a particular band that the new provider uses. All else aside, if the handset's radio can't use the band, then there is no connectivity on that band.
When a manufacturer update to a factory-unlocked phone I'd just bought hosed Band 17, I lost LTE on AT&T because 17 is the band they use here. I had EDGE, but no LTE.
Band 17 is an important one for AT&T. A phone that can't connect on 17 is next to useless on AT&T's service. So I returned the phone for a refund and bought an AT&T-branded phone by the same manufacturer, which had Band 17 intact, and it works fine. That's one of the advantages of using a carrier-branded phone: The carriers usually test the updates before pushing them to their phones. This is something that customers often complain about when waiting for the latest and greatest updates, but the delays are because the carriers don't want the updates hosing their customers' service.
This review of updates is something one should consider when pondering unlocking a carrier-branded phone and jumping ship to another provider. Once the phone moves, it no longer gets updates from its branded carrier. The updates from the new carrier may or may not adversely affect the phone at some future time. It's rare, but it's possible.
The other thing to consider is more fundamental, and that's whether the phone has the ability to operate on all of the bands used by the new carrier. If it does, then in theory, LTE should work fine. If it lacks a band or two, then it won't work where the "missing" bands are the only ones in use in a given area.
Similarly, if a tower in a given area is operating on multiple bands, but your phone lacks the least-congested of them, then it will only work on the more congested band(s). Will this matter? Maybe not. Most users won't notice anything other than that the connection is slower than it could be. But it will still be a sub-optimal experience, whether they notice it or not.
What it comes down to is that there's a lot of room between "works great" and "doesn't work at all." Ideally, the phone should be able to use
all the bands used by the "new" carrier. If it doesn't, then its functionality will be reduced accordingly. Whether the user ever notices depends on whether or not (or how often) they find themselves in areas served only by the "missing" bands.
As for OP's specific situation, there are multiple models of that handset with different band capabilities. They can be found
here.
Rich