I wonder if it's possible to 'clean up' an audio recording of a lecture from a smartphone, using some type of AI system?
Yes, it is possible. Usually the noise reduction is done using regular signal processing methods, such as spectral subtraction due to demand for low latency. But of course, modern methods of deep learning is applicable to this problem. For example variational autoencoder is the first that come to my mind, you can check this project. As another example you can look at this project , which is based on WaveNet.