To go to grad school in the states you will have to take either the
LSAT for Law School
or the GMAT for Business school
Which are the Law School and Business School equivalents of the SAT.
They ARE hard. Most people study for up to a year for them...and sometimes get tutors.
I would think that US schools will look very favourably upon LSE as it is a well respected university worldwide. I know someone who went to princeton who is now at Georgetown University Law School who did a year at LSE ... take that as you wish. As for employers, there is no denying that the bog standard american from the US heartland probably wouldn't have a clue what LSE was... they'd probs think it was some kind of disease. But, any good law firm or big business would realise that it was a good school. Most people tend to look at the UK education system very favourably. I know a guy who worked for Harvard Admissions and he is full of praise for UK education especially A levels.. go figure.Anyways...
Law School in the states is very stressful, and very competitive. My boyfriend is at Georgetown Law and god damn, i wouldn't wish the stress he has on my worst enemy. But saying this, it really depends on what law school you go to.. any of the top law schools are obviously going to be very stressful, lower down the scale then not so much.
Remember, it's VERY expensive, G'town Law is around $40,000 per year for three years of studying, plus living in Washington DC ontop of that.. and there is no guarantee you will get a scholarship.
However, again a Law Degree in the states is a really big thing... it's very prestigious and you will be sure (if you graduate from somewhere really good) to earn a lot of money once your through!
Hope any of that helps