Yes, you’re right, LTE uses more energy from battery, as you can see in the ‘Battery drain tests (3G vs 4G vs screen vs idle)’ http://androidforums.com/threads/battery-drain-tests-3g-vs-4g-vs-screen-vs-idle.502036/
In the author conclusions, there are also a lot of considerations to take into account.
From a more technical point of view, we can list some other reasons:
LTE networks uses 2G/3G for voice (unless we have VoLTE enabled). So it should remain in constant contact with those legacy networks to make/receive vocie calls/text messages when needed.
LTE devices periodically do searches to determine which cell it should be. With a typical combination 2G/3G/4G in different bands, it have a lot of networks to go.
LTE are not fully deployed everywhere, so chances are you’re more distant from the cell, and needs boost you transmission power.
LTE devices uses MIMO for multiple parallel transmissions. So, we have 2 RX/TX antennas (each with its own PA).
LTE technology has more complex - QAM and OFDM(A) requires more computing power/processors for modulating/demodulating the RF.