The evidence comes via a .plist file buried in an internal iOS test build from one of Apple’s major carrier partners. The .plist (Property List) file mentions LTE, a sure sign that there is some sort of LTE development being tested at that carrier.
BGR doesn't out the carrier, but it's not really a secret that Apple would want to support LTE eventually. However, one big bugaboo for Apple is battery life. Anything that sucks away battery life is a big no-no, and that's what LTE support would mean, right now.
iSuppli's recent teardown of the HTC Thunderbolt showed that the LTE chipset not only increased the cost of the device, it hogged real estate as well.
Size and cost would be a major factor in a decision against LTE in the fifth-generation iPhone, but also, second-generation Qualcomm LTE chips will be available in 1H2012. That chipset reduce both of those negatives, so that's is probably a good bet for when Apple would move toward an LTE version of the iPhone, the iPhone 6.
One thing's certain: someone is out there testing an LTE iPhone, already.