Mormons don't follow a liturgical calendar (unless, I suppose, you want to count Pioneer Day and the Sacrament Meeting Presentation), but that doesn't mean that individual Mormons can't follow one of their own. We've been celebrating Holy Week for years (although not Lent) and this year we're doing Advent. There are lots of different things you can do to observe Advent, but we have have four candles that we put in a circle and verses to read from the Bible and Book of Mormon and the Doctrine and Covenants. And since it's always nice when someone else organizes things for you, we're using this website. I'm quite sure that Christmas cookies will also make an appearance each week, thanks to the peppermint extract my mother mailed.
Holy Week is hard to do at home with just one family, but Advent is a lot more suited to independent observation which is perfect for us right now.