As a current student at Lawrenceville close with many of the faculty members, I think that I can give you a pretty good answer. Honestly, your chances are decent. Your grades and SSAT are well below the average applicant, and I would not be so sure to say that your interviewer loved you as they are purposefully as amicable as possible during the interview. Paying full tuition will help, but that will only get you so far. Assuming you had someone help you write your essays and they are, in fact, as good as you think, they could be a big boost to your application. Contacting coaches is always a big boost to the application through the way the admissions process works as well. All in all, you have an ok shot, but if you do not have any activities outside of athletics, that could really hurt your chances of getting in.