How to apply a different Loss function to one specific Label? I got a recurrent neural network in Keras, which classifies on 14 labels.
The first label is the most important one and should be predicted with the highest accuracy. The other labels don't have to be very accurate, they should just help the network to generalize better.

I thought of using the "Mean absolute error" for the first and the "mean squared error" for the other labels.

How can I integrate this in Keras?
Using mean absolute error might damage your output. You must do some regularization. One thing you can do would be to assign custom weights for each class metric.

Though in general, I would strongly advise against doing that. If this class is so important do separate model in one-vs-all fashion. Be aware you'll be overfitted.