I wouldn't honestly pick a bright patent leather bag for someone chronically ill. While I do agree a bright color is cheerful, maybe some bright nail polish to go with a more useful bag would be a better choice. Or a pomme wallet. I just don't honestly see where someone chronically ill would be getting dressed up enough or going out enough to use a bright red patent bag. It might make her feel worse - the having something beautiful and no place to use it thing. I think something comfortable, really useful, that she can keep and use for many years would be a much better choice. Eva is a nice choice too - it's light, comfortable, can be worn cross body, much less expensive (a gift is a great idea, but sometimes really expensive gifts can make a friend feel bad rather than good), and is just a wonderful bag for short little trips out (which is about what someone chronically ill can handle).
Something that is not hand-held, and is light and comfortable would be good too. Sometimes, while trying to be well-meaning, we can make a person feel worse, and it's important to be careful that we are not buying something we would want in a certain situation, rather than what would make the other person actually feel good and would be something they can use.
I vote for something not to expensive (so she doesn't feel bad about the cost), and something really nice, light and useful. You could buy something bright and pretty with it (fill up an Eva with gorgeous sprigs of flowers and baby's breath and include an invitation to take her to lunch.
I honestly think if I received a bright red patent bag for going out when I was chronically ill, it would just make me feel bad.