MinMaxScaler when LSTM predictions fall outside of training range?
Inverse-transforming with MinMaxScaler should be capable of producing something outside of the training data's range.  It seems that, in your use case, using a final activation that lands in $[0,1]$ might not be appropriate.  Even if you transform the training data to land in, say, $[0,0.7]$, applying a sigmoid or some-such on the final layer seems to lack motivation.

As to the question of whether it can be done: yes, just with a little roundabout thinking.  You can't specify what you want the scaler to think your data's max and min are, but you can specify the output range you want (parameter feature_range), which amounts to the same thing.