Hi zzzhound,
Welcome to the forum!
First of all, I think it's great you are doing this effort
May I ask for what defined reasons her friends think it is not good for her to get in a relationship? Are the arguments against you as a person (your character) or are all the arguments Lyme related? Has she or have they explained to you why exactly they are against the 2 of you together?
Trust is earned, but you need at least the opportunity to show that you can be trusted.
I think, but this is personal, that a relationship is between 2 people, it is their decision, and no one should intervene. It might be that her friends are doing this with the best intentions, but at the end it is about you 2.
I myself am in an interreligious and interracial relationship, although I don't like to define that at all: I'm married, that's it. If I would have listened to many people around me, I would not have married this guy. Meanwhile, we have been married for 10 years.
Members on this forum have lived so many different situations, relationship wise. There were break-ups, divorces, problems, but also many stories about couples that stood by eachother. Sometimes problems are Lyme related, sometimes it can be because of an already existing problem, and adding Lyme on top of it may be too much... My partners is suffering sometimes, but when I'm having an anger attack (I don't get physical lol) he says to himself 'it's not her. That's how he explaines it when I'm apologizing afterwards. He does a lot of household work too. These are just a few examples.
I think you should try to convince her that it is about you two, ask her to listen to her intuition, to what she feels, not to other people (don't put them down though, that might work against you, they have been her backup in the past and are a big part of her life). Maybe they are scared of loosing her as a friend? You can reassure her on that (that is if you are not planning to lock her up and prevent her from seeing her friends )
I myself am very straight forward if it is about people commenting a relationship, but that is because of what I lived. Maybe others on the forum will be more moderate in what they will advice you...