Converting JSON response into a GeoJSON layer in my Leaflet map

If you've loaded the response you can convert the shapePoints and elevationProfile arrays to an array of coordinate points that can be inserted in a blank GeoJSON feature object and loaded

// You can do it with a functional approach:
// Use Array.filter() to sort the alternating points to lats and lngs,
// then use Array.map() to extract the elevations
// and 'zip' the three arrays in one array of lng/lat/elev (x/y/z!) arrays
var lats = shapePoints.filter(function(e, i) {return i % 2 === 0;});
var lngs = shapePoints.filter(function(e, i) {return i % 2 != 0;});
var elevs = elevationProfile.map(function(e, i) {return e.height;});
var lnglats = lngs.map(function(e, i) {return [e, lats[i], elevs[i]];});

// or the more traditional way:
var lnglats = [];
for (var i=0; i<shapePoints.length; i=i+2) {
    lnglats.push([shapePoints[i+1], shapePoints[i], elevationProfile[i/2].height]);
}

geojson = {
    "type": "Feature",
    "geometry": {
        "type": "LineString",
        "coordinates": lnglats
    }
};

L.geoJSON(geojson).addTo(map);