There's absolutely no on-stage sex or romance, but that doesn't mean sex isn't important to Long Day's Journey. Mary, for instance, seems to have been emotionally paralyzed by her loss of virginity and by her decision to get pregnant with Edmund. For more on that, check out Mary's "Character Analysis."
It's not just Mary pulling sex into this play, either. Jamie seems to spend an awful lot of time down at the brothel, and he describes one encounter (the one with "Fat Violet") to his brother in Act IV. See Jamie's "Character Analysis" for a closer look at what exactly he gets up to at that brothel.