Когда input заполнен

$('#test1').change(function(){ 
    tmpval = $(this).val(); 
    if(tmpval == '') { 
        $('#lbl1').removeClass('class1'); 
    } else { 
        $('#lbl1').addClass('class1'); 
    } 
});

.class1 { 
  background: green; 
}

<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script> 
<input type="text" id="test1"> 
 <label id="lbl1" for="test1">поле 1</label>

$('#test1').on('change paste keyup', function () { 
  var $this = $(this); 
 
  var input_value = $this.val(); 
  var input_id = $this.attr('id'); 
 
  if (input_value.length === 0) { 
    $('label[for=' + input_id + ']').removeClass('foo'); 
  } else { 
    $('label[for=' + input_id + ']').addClass('foo'); 
  } 
});

.foo { 
  background-color: green; 
}

<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script> 
 
<input type="text" id="test1"> 
<label for="test1">поле 1</label>

document.getElementById('test1').onkeyup = function() { 
  if(this.value == '') { 
    document.getElementById('lbl1').classList.remove('class1'); 
  }else{ 
    document.getElementById('lbl1').classList.add('class1'); 
  } 
};

.class1 { 
  background: green; 
}

<input type="text" id="test1"> 
<label id="lbl1" for="test1">поле 1</label>