One of the most interesting elements of Julie, or the New Heloise is that the young lovers do not consider their sexual relationship in any way immoral. Because their union is marked by love rather than pure lust, the two view themselves as married in spirit, if not in the eyes of God. That the state and the church do not recognize them as married only serves to show the corruption of society, especially in regards to its relationship with the individual.
In general, Rousseau believed that society corrupts the inherent goodness of human beings. For Julie and Saint-Preux, society is a prison designed to keep them apart for arbitrary reasons of class, since Julie is noble-born and Saint-Preux is a commoner. By following their hearts in being together until Julie is compelled to marry the suitor her parents have chosen for her, they are defying a system that serves to thwart humanity's natural desires. In fact, after marrying de Wolmar, Julie is eventually torn apart by her conflicting desire to be faithful in her official marriage and her desire to be faithful to her true love. Had she and Saint-Preux been allowed to marry by the social forces hanging overhead, such a conflict need not have occurred.
As for comparisons with the presentation of ideas regarding nature and sexual love in Dangerous Liasions and Manon Lescaut, Julie is more akin to the latter than the former. Dangerous Liaisons operates very much within social structures, even as its characters behave abominably by society's agreed-upon standards. Manon, like Julie, presents a man versus society narrative, and its society-defying lovers are shown in a sympathetic light. Even when the lovers in that novel seek to find legal union in New Orleans, society still deigns to keep them apart.