First discovered this bug on iOS in my survival world. Placed a bed & lectern, cured a zombie villager and it turned to a librarian. I never traded with it once, but when I opened the trade window, it showed it had trade experience. Then when I destroyed the lectern, it didn't lose its profession.
Went on to a creative world and tested the bug. Placed a bed & lectern, spawned a zombie villager, then cured it. It turned into a librarian, but once I opened the trade window, it also showed that it had trade experience even though I never traded with it once. Then I removed the lectern but it didn't change into a regular villager.