I think you won at code golf.

It's that or two spaces at the end of every line.

ctrl-h \n \n[4 spaces]

Couldn't you stop at the first occurence of lastIndexOf === indexOf

var result
array.some(function(letter) {
    if(word.lastIndexOf(letter) === word.indexOf(letter) {
        return result=letter;
    }
}
return result;

I suppose that wouldn't match your ES6 exactly.

#!/usr/bin/env node
var readline = require('linebyline');
var lo = require('lodash');
function readFirstNonRepeatingOfStream(input,cb) {
 readline(input).on('line',function(line) {
  var counts = lo.countBy(line);
  Object.keys(counts).some(function(char) {
   if(counts[char] === 1) {
    cb(char);
    return true; //Breaks out of the loop.
   }
  });
 });
}
readFirstNonRepeatingOfStream(process.stdin,function(char) {
 console.log(char);
});