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Jessica is the daughter of Shylock, the rich Jew that Launcelot was employed under; hence, when in Act 2, Scene 3 it says that he is leaving Jessica's house, he is really leaving Shylock's house because he no longer wants to be under Shylock's employment. We are actually told his reasons for wanting to leave Shylock's household in the previous scene, Act 2, Scene 2, but we are actually not told many reasons and need to speculate about his reasons based on what we know of Jewish stereotyping.
Based on what Launcelot tells his father in Act 2, Scene 2, we know that Launcelot wants to leave Shylock's services because apparently Shylock treats him horribly. One thing Launcelot says, is that he is "famished in [Shylock's] service," meaning that he is underfed (98). In his opening soliloquy in Act 2, Scene 2, he declares that Shylock is "the devil himself" (22). We also know that Shylock is characterized according to stereotypes of Jews being greedy moneylenders who care more about revenge than about mercy. In short, we know that Shylock is characterized as being a very cruel person and that that is the reason why Launcelot wants to leave Shylock's house.
In Act 2, Scene 3, Shylock's daughter Jessica even helps characterize her father's cruelty in the line, "Our house is hell, and thou, a merry devil, / Didst rob it of some taste of tediousness" (2-3). Here, she is continuing Launcelot's metaphor of likening Shylock to the devil in the previous scene by referring to their house as "hell," which further characterizes her father's cruel nature. She also calls Launcelot a "merry devil," which refers to his role as a court jester. A court jester's job is to make the household laugh through devilish, or mischievous, witticisms and pranks. Hence, Jessica is ultimately saying that Launcelot is the one person who brought merriment into Shylock's household, putting an end to her weariness.
The errand Jessica gives Launcelot to do is also explained in Jessica's opening speech in Act 2, Scene 3. She knows that Lorenzo will be staying at Bassanio’s house, the house of Launcelot's new master, and so she gives Launcelot a letter to deliver to Lorenzo. Through this, we can see how Jessica prudently thinks up schemes to achieve what she wants. Portia also schemes and manipulates Bassanio, guiding him to choose the correct casket, so that she can win him as her husband. However, a difference between Portia and Jessica is that Portia's schemes align with her father's will permitting her to marry the man who chooses the correct casket, while Jessica schemes against her father's will as it would go against his religion to marry a Christian.