... gave DD a slightly lower "fake" lexile level for school
Some may say this does not seem right, but rather may represent a glass ceiling. Even when done as a way to help a kiddo choose age-appropriate reading material.
Are the books at school arranged only by lexile? Is there no way to find books to choose among, by genre? Fiction / Non-fiction? Biography? Historical Fiction? Nature? A parent can't take on every issue, but someone someday may wish to ensure kids at school can read up to their challenge level without undue concern they may find mature content.
Meanwhile it's great that she has a mom who appreciates her love of reading, so she can read up to her level outside of school. You may have already shared whether you are keeping a reading list, but I do not recall. Some parents like to keep a list of books their child reads... including lexile or reading level, and date. Such lists may prove valuable for future advocacy... for example substantiating interests, and/or demonstrating independent preparation or self-study in an area, when an opportunity arises which may have prerequisites. This may become important especially if the school has a lower lexile level on file.