LSTM train on varying length sequences
The solutions for sequences with different length are:

1- padding, but you do not want to.

2-truncate the sequences, so if you have for instance 3 sequences of different lengths you truncate the sequences so that they have all the length of the shortest one.

3- using timesteps of 1, but in this case your model will not learn the dependencies between different timesteps

4- using online learning with batch size = 1.

For the fourth solution this is an example in keras to create a random time-length batches of training data: Training an RNN with examples of different lengths in Keras. So you can have different batches with different lengths, and since you are using online learning with batch_size = 1 this can be a good solution. The fourth solution can also have advantages and disadvantages. For online learning the training is slower, but usually you need less epochs compared to sgd with batch size > 1 to have a good model. If you use stateful lstm, this could lead you to an unstable model, not always, but can happen.