Training a LSTM on a time serie containing multiple inputs for each timestep
The answer to this question highly depends on what relationship between the variables you are interested in.


If you are interested in the relationship between time and observation-value, treating the entities as different batches could make sense, under the assumption that the role of individual entities doesn't really matter to you. In this case, you would, for example, add the mean of each entity (or the overall mean) to all entities with missing values to get a constant number of observations per entity. But you could also simply average all values in each timestamp and include other features as min &amp; max. This would most probably deliver better results.
If you are interested in the relationship between entities and observation-value, this is a matter of missing data in time series. There are a lot of techniques that can help you with that from simply imputing the mean to more sophisticated methods like a Kalman filter. However, in the end, you will have to ask yourself why these observations are missing and choose the appropriate method. But since you are using time-dependent models in your experiment, I assume, this is not of interest to you.
If you are interested in the interrelationship of all three variables, you are dealing with panel data. In this case, I don't see a reasonable possibility to model this with an LSTM. Maybe another RNN-architecture could work, however, the only paper I found was Tensorial Recurrent Neural Networks for Longitudinal Data Analysis from Mingyuan et.al. But in the end, it would not matter, since an ARIMA-model also isn't appropriate for panel data. Usually, you use a Difference-In-Differences approach for that kind of data. In this case, I would suggest changing the dataset for your experiment.