We investigate variable-length data regression in an online setting and introduce an energy-efficient regression structure build on long short-term memory (LSTM) networks. For this structure, we also introduce highly effective online training algorithms. We first provide a generic LSTM-based regression structure for variable-length input sequences. To reduce the complexity of this structure, we then replace the regular multiplication operations with an energy-efficient operator, i.e., the ef-operator. To further reduce the complexity, we apply factorizations to the weight matrices in the LSTM network so that the total number of parameters to be trained is significantly reduced. We then introduce online training algorithms based on the stochastic gradient descent (SGD) and exponentiated gradient (EG) algorithms to learn the parameters of the introduced network. Thus, we obtain highly efficient and effective online learning algorithms based on the LSTM network. Thanks to our generic approach, we also provide and simulate an energy-efficient gated recurrent unit (GRU) network in our experiments. Through an extensive set of experiments, we illustrate significant performance gains and complexity reductions achieved by the introduced algorithms with respect to the conventional methods.