Here's what little information I know:
There shouldn't be any citizenship requirements (some European sued some time ago because you had to be a citizen to practise law in the US, he claimed it was unconstitutional, and either the US Supreme Court or a district court agreed with him). The main requirement is that you show proof of eligibility to be in the state where you want to take the bar (i.e. be a citizen, PR, or have lawful non-immigrant status). I'll agree, the process can get a bit confusing: I need to have a work permit to join the bar, I need a job to bother to apply for a work permit, I need the bar exam to get a job, so It's kinda cyclical but it's probably something that kinda all happens at once.
A long time ago when I was quite dumb in these matters, I read a post about non-citizens being able to write the bar in only a handful of states (NY, MA, CA to name a few). Ya, I freaked out and was like "dammit, I'm screwed." But after a little research, the post should have made better reference to non-citizens WHO WENT TO NON-ABA LAW SCHOOLS (actually, foreign law schools). That's the key; go to an ABA law school, do well enough that a firm sees fit to hire you, and you can write the bar... The next problem is...
This is the kick in the balls, really, for us Canucks. US immigration is really kind of demented, as I'm sure you know by now, and thus high-skilled professionals with post-undergrad degrees who speak English are not exactly let into the US with open arms (like they are in Canada or any other Western nation). That said, barring any family ties (i.e. a brother, child, or, if you're under 21 and unmarried, a parent who is/are a citizen), the only way you can get work authroisation in the US is through your employer.
Employer-based work permits:
There are 2 general ways that employers get skilled workers in the US (not counting intra-company executives and transferees, like if I was the CEO of Ford Canada and I went to work in the US, those are different visas):
This is not exactly a popular route. You need to be a person of exceptional skill (i.e. a nobel laureate) in the sciences, arts or entertainment to get a first-perference greencard application approved. Second on the pecking order are highly-trained executives and managers who either a) get a national interest waiver from the DOL (Dept. of Labor). or b) go through labour certification. Since law firms aren't exactly high-power multinationals, let's forget option a. Option b: labour certification is basically your company saying "there is no one in the US that can do this person's job, therefore we need to bring someone from abroad." Lets just say that, as a new grad from law school, labour certification won't be easily gotten. Ok, so immediate greencards are out, for now...
2. Non-immigrant work visas.
Ok, here's really the most common way. For highly-skilled workers, there is a wonderful visa called the H1-B visa, which is a 3-5 year work permit for highly-skilled occupations. A lawyer would probably fall under this category, so you'd think, ok thats hunky-dory. But, alas, there is a cap to the number of H1-B visas allowed to be issued every year, so, in all probability, by the time you graduate LS in April/May and get your stuff squared away for your job, the H1-B limit will be met.
Ok, so I'm screwed now, right?
Nope! Here is really the meat-and-potatoes of a Canadian immigrating into the US: the TN visa. Created because of NAFTA, these are instant, at-the-border work permits. You just show up at the airport or land crossing with a letter from your employer stating your job title, salary, give em some money and applications, prove that you are qualified (i.e. bring your diploma) and, presto, in 5 minutes you get work authorization. So why isn't there a mass exodus of canadians south of the border in search of warmer weather and better work opportunities? TN visas are only given to certain categories of professionals. Simple "ad agency rep", "director of marketing" types wont get in. Luckily, lawyers are in the class of TN visas. And, the best part is, the requirement is a law degree OR bar membership. Note the OR, there... you just have to have a JD to be eligible for the TN.
So, that's really the rundown of the work-permit options.
After you've been in the states for a while, your employer begins the process of applying for a greencard for you. Or, as has been pointed out, marriage into one is a distinct possibility since you will be living amongst bachelorettes and you're in your marriage-prime years. Honestly, I don't know much about long-term job prospects and work authorisation...
And, lastly, the F1 visa, which you enter the US on to study at law school, gives you 12 months of something called OPT, optional practical training. This is basically a degree/program of study-specific work authorisation for 12 months during your educational program (think summer associate) or after you have completed study. The total is 12 months, so 2 summers cuts into that 12-month period, but there's also another option called CPT (curricular practical training) which may be used as well -- your school's international centre (not LS, the main university) has tons of information on this stuff.
and, for good measure:
GOING BACK TO ICE-LAND:
Assuming you want to go back to Canada to put your law degree to work as a lawyer, you'll need to join a provincial law society. Ok, this isn't exactly as easy as "I'm canadian, here is my US law school degree, now let me practise." In Canada there is a bit more elitism/protection of the law profession, and it basically means that:
a) you might have to go back to a canadian law school for 1-3 years to pick up some courses pertaining to Canadian-flavour common law (just like, at the beginning with those 4 states: other state bars require a LLM as a supplimentary degree for foreign-degreed lawyers)
b) they will find a way to extract their one year of slavery (sorry, i meant to say articling period) from you. Unless you've been a practising attorney for many years, if you're fresh out of law school, they're going to hit you up for a year of indentured servitude.
so, my suggestion about this: if you're reasonably sure about wanting to return to canada, or even if you're 50/50, pick up as many generic law courses as you can (property instead of american constitutional law) and maybe some comparative/international stuff if ur LS has it. Also, check out http://www.flsc.ca/en/foreignLawyers/guidelines.asp
which has the info pertaining to US law degrees. A caveat though: foreign lawyer accreditation is probably very political/idiosyncratic, hence the information on that link is somewhat vague.
Anyhoo, sorry for the unsolicited, verbose and VERY lengthy post. I hope it helps some. A final note, don't quote me on any of this or assume that I'm a trained professional in any of these matters, this is just the result of looking around for this kind of information.