In general, the clause “Lacking medical education,” in the first sentence, implies that the reason the broker does what she does is that she lacks medical education. You could make this fairly weak implication explicit with something like, “Because she lacked medical education,” or “Due to her lack of medical education, ....”
In the second sentence, adding “Despite” to the clause changes the meaning, so that now, lacking medical education is a reason not to do what she did. This is similar to writing, “Although she lacked medical education,” or “She lacked medical education, but nevertheless, ....”
In this specific context, either giving the advice only because she lacked medical education or giving the advice even though she lacked medical education is critical of her, and implies she should not have spoken. However, the first sentence implies that she is ignorant about monkeypox. The second is more neutral about whether she could be right anyway.