Have you tried waiting until leader training is finished and then re-attempting new psi training?

Yes, The only way I managed to fix it was by completely removing the Psi lab and rebuilding it. I'll try and replicate this from an old save later today and post the method here.

Edit: I've just replicated the issue on an old save, here are the steps which caused it for me.

#1 Start Psi training for a unit
#2 Pass some time to reduce the training length
#3 Make this Unit start training to become a leader while still training in the Psi lab
#4 Pass time, the Psi training will complete while the leader training is still ongoing. Select Continue Training - At this time I noticed that nothing appeared in the continue training window.
#5 Pass time until the leader training is finished.

Apon returning to the Psi lab you'll see the Unit as if it's currently training but selecting the dropdown to replace/cancel has no effect.

We double-checked and the code is supposed to prevent you from initiating leader training while still training in the psi lab. We'll investigate and try to run down what's going on. Thanks for the report.

I got the opposite: the leader is stuck in Leadership training because I carelessly put her into Psi training at the same time. Sadly, I am in Ironman, so I cannot pull a save. I'll tr"resolution through destruction" technique.