Lorenzo's plan is that Jessica should dress up as a boy and then be his torchbearer during a street festival. In this way, nobody would notice her and her camouflage would make others believe that she is his male assistant. Added to this is also the fact that festival-goers would be wearing masks which would not only hide Jessica's real persona, but would also mask his.
In Act 2, scene 6, Lorenzo arrives at Shylock's penthouse where his friends, Salarino and Gratiano are already waiting. He thanks them for their patience and assures that he will do the same for them should they ever need assistance in 'stealing' a wife. He then calls on Jessica who appears at the window and asks him to identify himself.
Jessica has already prepared for the elopement and now that her father, Shylock, has left, the moment is most opportune for her escape. She has already put on a boy's attire and is quite embarrassed about the fact, as shown in the following extract:
Here, catch this casket; it is worth the pains.
I am glad 'tis night, you do not look on me,
For I am much ashamed of my exchange:
But love is blind and lovers cannot see
The pretty follies that themselves commit;
For if they could, Cupid himself would blush
To see me thus transformed to a boy.
Jessica believes that even Cupid, the god of erotic love, attraction and affection, would be ashamed to see her changed into a boy. Lorenzo tells her to come down for she has to be his torchbearer. Jessica is practically mortified by the idea, for she believes that she has to 'hold a candle' to her shame. She does concede, however, that her shames mean nothing against the discovery of her love. She says that her identity should be hidden, though.
Lorenzo assures her that she is well disguised as a boy and compliments her. He urges her to hurry for the darkness ensures their secrecy. Jessica goes to fetch more of Shylock's money. In her absence, Lorenzo confirms his love for her to his two friends ans states:
...Shall she be placed in my constant soul.
Jessica returns and joins them after which she, Lorenzo and Salarino leave the scene.
The reason why the two lovers make such complicated arrangements to elope is because Jessica's father, Shylock, is a Jew who hates Christians. A relationship, never mind a marriage, between his daughter and Lorenzo, a Christian, would be akin to a betrayal. Furthermore, Jessica has also stolen many of her father's valuables, which, we discover later, are of greater importance to him than his daughter who he, shockingly, wishes to be dead. He'd rather have his ducats and his stolen possessions back, than her.