Yes, but there's no phone that gives you LTE both here and there. And if it's the Note 3 (is this the device for your Aunt from the laptop forum?) there's a bit of an issue with region locking.
(The region lock is disabled by using a device in the home region on a home-area SIM for a few minutes before you leave. That's great for a UK device that you start using in the UK, but for one you start using in the US, oops. I believe the region lock doesn't actually forbid US/Europe cross-regional use, but it's not something I'd want to mess with.
So you could get a US model and start using it here (but it wouldn't have LTE for over there, just HSPA+), or a UK model and wait to start using it until you're back, but probably not both.)
If it's not the Note 3, you're still left with the LTE here/LTE there issue, but all you need to worry about is making sure it's SIM-unlocked.
The biggest US sellers of non-US phones are
Negri Electronics
Expansys
and of course US Amazon