I am not aware of a modern rule. There are still some kick backs from an old rule which states that the participles end in 't' whilst the active verbs end in 'ed'. For example:
She has cookt a cake.
She cooked a cake.
This still exists with 'to learn'.
I learned a lesson.
I have learnt a lesson.
Therefore, the term "lessons learned" can be written "lessons learnt" too, depending on what you understand the missing words to be.
For example:
Lessons (which we) learned
Lessons (which we have) learnt
Modern usage has blurred to lines now, and I judge there to be no rule these days.