1. Make the left margin narrower and use a paragraph style with left indentation for all lines (can also be done via the horizontal ruler).
2. Insert the background colour as a drawing (Object > New drawing; Rectangle with filling, no lines, Layout: Move with text; text wrapping: behind text). This can reach into the margin.
Personally, I would prefer the second way. Then you can fine-tune the background area and, if there are several key messages in the document, simply copy and paste the background.