gistfile1.txt

var flatten = function(data) {
    var result = {};
    function recurse (cur, prop) {
        if (Object(cur) !== cur) {
            result[prop] = cur;
        } else if (Array.isArray(cur)) {
             for(var i=0, l=cur.length; i<l; i++)
                 recurse(cur[i], prop ? prop+"."+i : ""+i);
            if (l == 0)
                result[prop] = [];
        } else {
            var isEmpty = true;
            for (var p in cur) {
                isEmpty = false;
                recurse(cur[p], prop ? prop+"."+p : p);
            }
            if (isEmpty)
                result[prop] = {};
        }
    }
    recurse(data, "");
    return result;
}
var flattenObject = flatten(tree);

var total = 0;
for (var prop in flattenObject) {
  if(prop.indexOf('precio_linea')>0){
    total += parseFloat(flattenObject[prop]);
  }
}

console.log(total.toFixed(2));

gistfile2.txt

➜  a node app2.js
{ '0.id': '201724171830',
  '0.parent': '',
  '0.piezas': ' 10',
  '0.precio_linea': '22.50',
  '0.children.0.id': '20172515426',
  '0.children.0.parent': '201724171830',
  '0.children.0.piezas': ' 10',
  '0.children.0.precio_linea': '50.50',
  '0.children.0.children.0.id': '201725123623',
  '0.children.0.children.0.parent': '20172515426',
  '0.children.0.children.0.piezas': ' 10',
  '0.children.0.children.0.precio_linea': '34.21',
  '0.children.0.children.1.id': '201724171631',
  '0.children.0.children.1.parent': '20172515426',
  '0.children.0.children.1.piezas': ' 10',
  '0.children.0.children.1.precio_linea': '34.21',
  '0.children.0.children.2.id': '20172515548',
  '0.children.0.children.2.parent': '20172515426',
  '0.children.0.children.2.piezas': ' 10',
  '0.children.0.children.2.precio_linea': '34.21',
  '1.id': '201724194033',
  '1.parent': '',
  '1.piezas': ' 10',
  '1.precio_linea': '34.21' }