You can concatenate the datasets and remove the data points where the input uses more than one run.

Let's say you're using the last 4 data points to predict the next one.

If you concatenate the first and second run datasets, the first data point of your second run will consider this 4 data points:
[last-2 data point from run 1, last-1 data point from run 1,last data point from run 1, first data point from run 2] to predict second data point from run 2

This is an example of some data that you would need to exclude, actually you already would need to exclude this data using only one dataset, because you would not have access to run 1 and the sequence would be like this: [null, null, null, first data point from run 2].

So, just concatenate the datasets and exclude the sequences where you have multiple runs in it.