I agree with your logic - it looks completely non-parallel to have Lucy without the bullet. An important part of knowing the rules of style is knowing when to break them. However, are bullets strictly necessary under each heading?
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If I have a single point, I indent it to make the bullets but do not give it a bullet point because bullet points are, strictly speaking, for lists.
While the first answer became impractical because of the example given, they are correct, you must know when to break the rules. It is practical for your use to keep the bullet even though you do not technically have a list. I'm certain no one will notice besides you but if you leave out the bullet everyone will notice and probably complain.
Whilst it is true that some answers are years after the question was posed, as a new user of the site I found the discussion of the issue useful. I was considering if using a single bullet point to subtly highlight a paragraph in a standard letter we send out to dozens of people a week would be a reasonable method.
(My conclusion is that, whilst not usual unless there is a list, it is a