TensorFlow Lite now supports key features for training (e.g. variables) as you can see in the document
As you can see in the training code example, you can use tf.lite.OpsSet.SELECT_TF_OPS when using the TFLiteConverter to enable this feature.
It seems to me that the ops required to train AvePool3D
are all includeded.
Let us know if you have any further questions.