You will have to jump through a bunch of hoops to get it working and it would in NO WAY BE SUPPORTED, not to mention that you WILL VOID ANY WARRANTY as well.
It will not work the other way around as far as I know. And need I mention that any modification is 100,000% at your own risk, I can and will not be liable for anything that may or may not happen should you undertake the operation.
BTW LTE basically uses the GSM bands and the Verizon phones that are "global" have GSM available but turned off for use in the USA. But most of the Verizon phones are stuck to Verizon.