Максим Ученик,
var slider = $(".slider").slick({
infinite: true,
slidesToShow: 1,
slidesToScroll: 1,
dots: true
});
var lis = [...document.querySelectorAll(".slick-dots li")];
lis.forEach((el,i) => el.addEventListener("mouseenter", () => slider.slick("slickGoTo", i)));