The essence of this scene is Portia's inability to choose a husband based on love and attraction and, more important, she recognizes that her larger fate is not in her control:
In terms of choice I am not solely led/By nice direction of a maiden's eyes;/Besides, the lottery of my destiny/ Bars me the right of voluntary choosing. . . .
Portia acknowledges that her choice of husband has nothing to do with attraction ("nice direction of a maiden's eyes") but is in the control of destiny or fate in the form of the lottery her father has created in order to "choose" her husband. In a larger sense, however, Portia is articulating the realization that one of the most important events in her life--the selection of her husband, which will determine the quality of her life going forward--is in the hands of destiny or fate--in other words, nothing she can do will have an effect on the outcome.
Portia's lack of control, and her own role in that lack of control, becomes even more apparent in the next several lines:
But if my father had not scanted me/And hedg'd me by his wit, to yield myself/His wife who wins me by that means I told you. . . .
The word scanted is a form of scanned, which, in Elizabethan times, meant "to examine closely," Portia is complaining that she would have been better off had her father not questioned her closely about her feelings, and then used his wit to convince her to go along with the idea of the lottery. She is undoubtedly wishing that she had told her father how she really feels about the lottery. It is worth noting here that Portia's situation--not being able to choose her marriage partner--was fairly standard Elizabethan marriage practice among the middle and upper classes--marriages were not viewed as "love matches" but were more often the result of what, in effect, was a business decision on the parents' part to make sure their children would marry advantageously. In short, love was not part of a parent's calculation when choosing a mate for his or her child.
Shylock's lottery accomplishes at least two important goals: 1) By using a lottery for the eligible suitors, Shylock avoids the complications inherent in showing favoritism to one family. And from a business perspective, this is an important success since he depends on the willingness of others to do business with him--the lottery, because it is based on chance, takes away Shylock's potential for alienating someone powerful; 2) Shylock's use of the lottery also takes away his responsibility to his daughter--if the lottery his based on chance, and Portia's marriage turns out badly, Shylock is absolved from responsibility because destiny or fate is the responsible party.