I'm sorry - but I disagree with the 4L. First, law schools do not report LSAT for their 2nd year students. What's reported to the ABA (and USNWR) is INCOMING first year LSAT scores. That's the whole appeal to transferring for those who may not have scored well on their LSAT the first time. They excel during their first year, and can transfer to a better school on grades and recommendations. These things have greater weight than LSAT, IF the LSAT is even considered at all by the new law school. Law schools look to transfer students to find qualities desired by the school to fine tune their class. They can accept them without jeopardizing their rankings should the transfer student have a "low" LSAT. Also, transfer students who do really well in their first year have a good chance of passing the bar on the first try, which IS considered in the school's ranking.
I don't understand how the topic shifted to LSAT from the question about transferring from a 3rd tier to a higher ranking school. Do tell me what law school will consider the LSAT score of a transfer applicant over their grades and professor recommendations.