I try to style a LineString in a Mapbox Map through L.Geojson and all the style properties I could find are: fillColor, colour, weight, opacity. Does anyone know if there is something else? For example to add a border width, a colour to this border, dashed the line, etc. ?
Mapbox.js uses the simplestyle spec. That's where you can find out more about defaults and accepted values.
Adding a dashed line is a little more complicated, see dashArray in the leaflet documentation which will work with mapbox.js.