Convolutional long short-term memory (ConvLSTM) possesses a remarkable capability of encoding spatial information and capturing long-range dependencies in sequential data. As a result, ConvLSTM has garnered success in hyperspectral image (HSI) classification. Nonetheless, the design of the special gate structures and convolution operations contributes to a high model complexity, making it challenging to deploy in resource-constrained environments. In this article, we propose a fully tensorized ConvLSTM model for HSI spatial-spectral classification under the premise of low complexity. First, we devise a novel and efficient tensor-sequenced convolution in the tensor train (TT) format, called ETTConv. ETTConv can reduce the number of parameters and computations in the standard convolutional layer by tensorizing the convolution kernels and mapping them to a series of smaller ones. Building upon this innovation, we present a novel ETTConvLSTM unit, formed by jointly compressing all weight tensors within the recurrent units. Using it as the fundamental unit, we construct the lightweight a efficient tensor train ConvLSTM 2-D neural network (ETTCL2DNN) model, characterized by reduced complexity without compromised classification performance. Furthermore, to better preserve the joint spatial-spectral structure of HSI data, we extend the ETTConv layer and the ETTConvLSTM unit to their 3-D versions, resulting in a new lightweight a efficient tensor train ConvLSTM 3-D neural network (ETTCL3DNN) model. Extensive quantitative experimental results on three widely used HSI datasets demonstrate the superiority of the proposed methods, exhibiting enhanced classification performance with reduced model complexity.