I wrote a helper function for this:

function intersection() {
  var result = [];
  var lists;

  if(arguments.length === 1) {
    lists = arguments[0];
  } else {
    lists = arguments;
  }

  for(var i = 0; i < lists.length; i++) {
    var currentList = lists[i];
    for(var y = 0; y < currentList.length; y++) {
        var currentValue = currentList[y];
      if(result.indexOf(currentValue) === -1) {
        var existsInAll = true;
        for(var x = 0; x < lists.length; x++) {
          if(lists[x].indexOf(currentValue) === -1) {
            existsInAll = false;
            break;
          }
        }
        if(existsInAll) {
          result.push(currentValue);
        }
      }
    }
  }
  return result;
}

Use it like this:

intersection(array1, array2, array3, array4); //["Lorem"]

Or like this:

intersection([array1, array2, array3, array4]); //["Lorem"]

Full code here

UPDATE 1

A slightly smaller implementation here using filter

Destructive seems simplest, especially if we can assume the input is sorted:

/* destructively finds the intersection of 
 * two arrays in a simple fashion.  
 *
 * PARAMS
 *  a - first array, must already be sorted
 *  b - second array, must already be sorted
 *
 * NOTES
 *  State of input arrays is undefined when
 *  the function returns.  They should be 
 *  (prolly) be dumped.
 *
 *  Should have O(n) operations, where n is 
 *    n = MIN(a.length, b.length)
 */
function intersection_destructive(a, b)
{
  var result = [];
  while( a.length > 0 && b.length > 0 )
  {  
     if      (a[0] < b[0] ){ a.shift(); }
     else if (a[0] > b[0] ){ b.shift(); }
     else /* they're equal */
     {
       result.push(a.shift());
       b.shift();
     }
  }

  return result;
}

Non-destructive has to be a hair more complicated, since we’ve got to track indices:

/* finds the intersection of 
 * two arrays in a simple fashion.  
 *
 * PARAMS
 *  a - first array, must already be sorted
 *  b - second array, must already be sorted
 *
 * NOTES
 *
 *  Should have O(n) operations, where n is 
 *    n = MIN(a.length(), b.length())
 */
function intersect_safe(a, b)
{
  var ai=0, bi=0;
  var result = [];

  while( ai < a.length && bi < b.length )
  {
     if      (a[ai] < b[bi] ){ ai++; }
     else if (a[ai] > b[bi] ){ bi++; }
     else /* they're equal */
     {
       result.push(a[ai]);
       ai++;
       bi++;
     }
  }

  return result;
}

You could use Array.filter:

var result = arr1.filter(function(n) {
  return arr2.indexOf(n) > -1;
});

I have a simple one-liner approach:

const res = Object.values(object).reduce((a, b) => a.filter(i => b.includes(i)))

But since you want it in ES5 (ECMAScript 2009) version, that means no arrow functions, no includes(), and no usage of Set objects.

const res = Object.values(object).reduce(function (a, b) { 
  return a.filter(function(i) {
    //return b.includes(i);
    return b.indexOf(i) >= 0;
  });
});

console.log(res);