file.readLine ?

There's nothing built-in, but I did do something for the laser cutter that worked quite well. I just stripped it down for you below:

function readLines(fileName, lineCallback, completeCallback) {
  var f = E.openFile(fileName);
  var buffer = f.read(64);
  if (buffer===undefined) {
    console.log("Couldn't load file");
    completeCallback();
    return;
  }
  
  function newLine() {
    // get new data from file  
    while (buffer.indexOf("\n")<0) {
      var r = f.read(64);
      if (r===undefined) {
        f.close();
        break;
      }
      buffer += r;
    }
    // if we didn't get any data, finish...
    if (buffer==="") return completeCallback();
    // get new line
    var eol = buffer.indexOf("\n");
    if (eol<0) eol = buffer.length;
    var line = buffer.substr(0,eol);
    buffer = buffer.substr(eol+1);
    lineCallback(line);
    setTimeout(newLine, 1); // next line on idle
  }    
  newLine();
}