Let a user U with 3 possible states: A, B and C. From A you can go everywhere (including A), from B or C you can only go to A. LSTM are a good to model Markov-problems with an extra notion of long term memory across steps.
But if I understand right, we need to have one model per user ? So how does the training looks like ?
Answering your question does not need to consider LSTMs or even the particular kind of problems you are describing, since it applies to any kind of problems related to predicting something per individuals.
If you need to predict something for each individual in your dataset, then basically there are three possible approaches: (1) build individual model for each person, (2) build a global model for the whole population ("on average" predictions), or (3) build a model for a whole population that accounts for the individual differences. The first two approaches are potentially problematic, you risk overfitting in the first case and underfitting in the second one. The problem is nicely explained in the guest post on Andrew Gelman's blog entry Everything I need to know about Bayesian statistics, I learned in eight schools. Usually the most fruitful approach is the "hierarchical" model that shrinks the individual predictions to the global average. In your case this would mean building a model for all the individuals and using some features that explain the individual-level variability.
