is in-educable. And I don't believe, based on what we have seen so far, that Lucy doesn't want to learn. From Chapter 22 we have the following description of Lucy's abilities:

Lucy was naturally clever; her remarks were often just and amusing; and as a companion for half an hour Elinor frequently found her agreeable; but her powers had received no aid from education, she was ignorant and illiterate, and her deficiency of all mental improvement, her want of information in the most common particulars, could not be concealed from Miss Dashwood, in spite of her constant endeavour to appear to advantage. [emphasis mine]

We also have direct evidence in that Lucy knows exactly how to flatter Lady Middleton in order to have her visit to Barton Park extended. She also knows when Anne is being overly familiar and shuts her up (although she does it in a rude manner).