What does it mean to dream about carrying your dead grandmother around on your shoulder who is alive in the dream and wants to lay down in a bed and want speak?

It means that you feel that you didn't spent enough time with her before she died. Or perhaps you miss a lot of things from her. But it doesn't mean that she want to say something important to you or wanting to deliver extra ordinary message to your family.

The metaphor of carrying something or someone around on your shoulder or back refers to your feeling responsible for that burden. In your dream, your deceased grandmother feels like a burden to you, and you have a sense of responsibility or guilt. But in your dream she wants to lie down; that is, she wants you to put her down, to stop bearing responsbility or guilt because of her. In the dream she also wants to speak, suggesting that she has information, probably about your sense of guilt. Altogether, this dream strongly suggests that there is information you need to learn about your grandmother that will help you put down this burden of guilt.