I think JA had the same negative attitude towards Lady Jane Grey, that she had towards Henry VII, and I think the reason can be found in Goldsmiths text.

Here's what JA has to say about Lady Jane Grey in the Henry VII paragraph:

Lady Jane Grey....was yet an amiable young woman & famous for reading Greek while other people were hunting.

This following extract is from Letter XXXIII of Goldsmith's history:

...Jane Grey was attached to the reformers;( the Protestants-JW) though yet but 16 her judgement had attained such a degree of perfection as few enjoy in their more advanced age. All historians agree that the solidity of her understanding improved by continual application rendered her the wonder of her age. Ascham, tutor to Elizabeth, informs us that coming once to await upon her father’s house in Leicestershire, he found her reading Plato’s books in Greek when all the rest of her family were hunting in the park. He seemed surprised at her being the only person absent from the diversions abroad but she assured him that Plato was a higher amusement to her than the most studied refinements of sensual pleasure

I can almost imagine hearing JA’s teeth grind as she reads this chapter. It rather reminds me of Emma’s reaction to the almost perfect Jane Fairfax:

Why she did not like Jane Fairfax might be a difficult question to answer; Mr. Knightley had once told her it was because she saw in her the really accomplished young woman, which she wanted to be thought herself; and though the accusation had been eagerly refuted at the time, there were moments of self-examination in which her conscience could not quite acquit her.

Emma :Chapter 20