If you want to mix 3D and mapbox to draw freely some 3D lines, I would recommend you to use the latest version of threebox a three.js plugin for mapbox.
You'll able to draw different rect or curved lines with origin destination like this...

Once you define your line geometries, you can add them with only a few lines of code in your page:
map.on('style.load', function() {
map.addLayer({
id: 'custom_layer',
type: 'custom',
renderingMode: '3d',
onAdd: function(map, mbxContext){
tb = new Threebox(
map,
mbxContext,
{defaultLights: true}
);
for (line of lines) {
var lineOptions = {
geometry: line,
color: (line[1][1]/180) * 0xffffff, // color based on latitude of endpoint
width: Math.random() + 1 // random width between 1 and 2
}
lineMesh = tb.line(lineOptions);
tb.add(lineMesh)
}
},
render: function(gl, matrix){
tb.update();
}
});
});