JSFiddle - React, Tailwind, and code Playground

HTML

<script src="https://cdnjs.cloudflare.com/ajax/libs/lodash.js/3.9.3/lodash.min.js"></script>

JavaScript

var outer = [{
  "name": "T1",
  "inner": [{
    "type": "DAY"
  }, {
    "type": "MONTH"
  }, {
    "type": "WEEKLY"
  }]
}, {
  "name": "T2",
  "inner": [{
    "type": "DAY"
  }, {
    "type": "MONTH"
  }, {
    "type": "WEEKLY"
  }]
}];

var b = _.sortBy(outer, function(o) {
  return o.name;
});

// outer array
outer.map(function(obj) {
  console.log(obj.inner);
  console.log('*********************');
  // inner array
  obj.inner.map(function(budObj) {
    // do something to sort here //
  });
});