Horizontally layering LSTM cells
However, I couldn't find anything about horizontal LSTM cells, in which the output of one cell is the input of another.

This is the definition of recurrence. All RNNs do this.
I am pretty new to the whole neural network scene, and I was just going through a couple of tutorials on LSTM cells, specifically, tensorflow.
In the tutorial, they have an object tf.nn.rnn_cell.MultiRNNCell, which from my understanding, is a vertical layering of LSTM cells, similar to layering convolutional networks. However, I couldn't find anything about horizontal LSTM cells, in which the output of one cell is the input of another. 
I understand that because the cells are recurrent, they wouldn't need to do this, but I was just trying to see if this is straight out possible.
Cheers!