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I am working in a different city, in a different state, than where my law school is located, making it near-impossible for me to personally see a professor to request a LOR. Do you guys have any suggestions or recommendations on the best way to put together an email to request an LOR (successfully)?

I'd appreciate any input.

I guess it would help to know how well you know the professor in question...

Just e-mail and ask (politely), offering things like resume/writing sample to provide further information. There's no set formula and as long as you're polite it really doesn't matter how you ask.