Choosing a suitable learning rate based on validation or testing accuracy?
You cannot select a parameter based on test accuracy, because the moment you do that, it becomes a validation accuracy as it has affected the final model. Therefore, you are always choosing based on validation accuracy. 

As a result, the best result comes from learning rate 0.001, with the highest validation accuracy 0.6900. We have ignored Testing accuracy. If we select based on Testing accuracy, it becomes a validation accuracy.

Generally, a learning rate that is a looser at epoch 50, might be a winner at epoch 200. In other words, a slower convergence may lead to a higher accuracy. Therefore, this issue is worth considering too.