Edit in JSFiddle

<div class="wrapper">
  <ul class="slider slider--big1">
    <li class="slider__item">1</li>
    <li class="slider__item">2</li>
    <li class="slider__item">3</li>
    <li class="slider__item">4</li>
    <li class="slider__item">1</li>
    <li class="slider__item">2</li>
    <li class="slider__item">3</li>
    <li class="slider__item">4</li>
  </ul>
</div>
<div class="wrapper wrapper--small">
  <div class="prev">Назад</div>
  <ul class="slider slider--small">
    <li class="slider__item">1</li>
    <li class="slider__item">2</li>
    <li class="slider__item">3</li>
    <li class="slider__item">1</li>
    <li class="slider__item">2</li>
    <li class="slider__item">3</li>
  </ul>
  <div class="next">Вперед</div>
</div>
<div class="wrapper">
  <ul class="slider slider--big2">
    <li class="slider__item">1</li>
    <li class="slider__item">2</li>
    <li class="slider__item">3</li>
    <li class="slider__item">4</li>
    <li class="slider__item">1</li>
    <li class="slider__item">2</li>
    <li class="slider__item">3</li>
    <li class="slider__item">4</li>
  </ul>
</div>
.wrapper {
  width: 360px;
}
.wrapper--small {
  width: 240px;
  margin: 0 60px;
  position: relative;
}
.prev {
  position: absolute;
  left: -60px;
  width: 60px;
  height: 60px;
  line-height: 60px;
  font-size: 12px;
  cursor: pointer;
  top: 50%;
  transform: translateY(-50%);
}
.next {
  position: absolute;
  right: -60px;
  width: 60px;
  height: 60px;
  line-height: 60px;
  font-size: 12px;
  cursor: pointer;
  top: 50%;
  text-align: right;
  transform: translateY(-50%);
}
.slider__item {
  width: 60px;
  height: 60px;
  border: 2px solid #000;
  display: flex;
  flex-direction: row;
  align-items: center;
  align-content: center;
  justify-content: center;
  text-align: center;
  font-size: 20px;
  font-weight: bold;
  color: #000;
  -webkit-box-sizing: border-box;
  -moz-box-sizing: border-box;
  box-sizing: border-box;
}
$(document).ready(function(){
  var slider = $('.slider--big1').lightSlider({
  	item: 6,
    pager: false,
    controls: false,
    slideMargin: 0,
    slideMove:2,
    loop: true,
    enableDrag: false,
    enableTouch: false,
    prevHtml: 'prev',
    nextHtml: 'next',
  });
  var slider2 =   $('.slider--small').lightSlider({
  	item: 4,
    pager: false,
    controls: false,
    slideMargin: 0,
    slideMove:2,
    loop: true,
    enableDrag: false,
    enableTouch: false,
    prevHtml: 'prev',
    nextHtml: 'next',
  });
  var slider3 = $('.slider--big2').lightSlider({
  	item: 6,
    pager: false,
    controls: false,
    slideMargin: 0,
    slideMove:2,
    loop: true,
    enableDrag: false,
    enableTouch: false,
    prevHtml: 'prev',
    nextHtml: 'next',
  });
  $('.prev').click(function(){
    slider.goToPrevSlide(); 
    slider2.goToPrevSlide(); 
    slider3.goToPrevSlide(); 
  });
  $('.next').click(function(){
    slider.goToNextSlide(); 
    slider2.goToNextSlide(); 
    slider3.goToNextSlide(); 
  });
});