No. The iPhone 5 was the first LTE capable iPhone.
The original iPhone was only capable of GSM/EDGE. The iPhone 3G was capable of, you guessed it, 3G, or HSDPA. The iPhone 3GS was capable of of 7.2 Mbps HSDPA. The iPhone 4 was basically the same, network wise, as the 3GS, but a mid-year refresh of it brought along the first CDMA capable iPhone, but was only CDMA 1x and CDMA EVDO. The iPhone 4S brought along the first "all-in-one" iPhone, being that it was both GSM and CDMA capable all in the same device, where-as before the 4S(and after), you had to get a separate device to use the other network technologies. And the 4S also included HSPA+, which is what may have made a lot of people think that it was LTE capable, because iOS 6, I believe, brought along a "4G" network indicator, but only on AT&T. Then the iPhone 5 rolled out, which brought along LTE connectivity. And the rest is history (all newer models i.e. 5S, 6, 6S, all brought along added LTE bands and capabilities like CA and VoLTE).
Just a quick history lesson, if anyone is interested.
-Anthony