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So I'm facing a situation that's probably a bit odd but the opinions I've received on this website in the past have really helped in my decisions so far, although in a way those decisions have led to my current situation.

I finished 1L at HYS and I'd say things went pretty well, I love my classmates and professors. I'm currently working for a firm on the west coast but the thing is I don't really find the work that interesting and a lot of the time I felt bored with law school.

My background is in finance. I have a degree in econ from HYP and also a masters that I got in the UK. I lived abroad before law school dealing with debt restructuring etc. I thought I would go to law school and work at a firm and eventually end up back in finance, but I feel like I am taking the long route now that I know what it's like. Luckily I know some people in the industry and was able to get an interview at Lazard in their restructuring group. The person that put me in contact says there are going to be taking on a huge client in Europe and they need people with experience in the particular country I've worked in. Job would pay well etc, and I feel that I'd probably be happier.

So if I get the job offer, what are the potential long term effects of quitting half way through my SA and dropping out? The people at my career services office and the deans I've spoken to all appear to be biased because they insist on my working through the summer and enrolling next semester.

I'd say you should definitely finish the summer - that just seems professional. As to whether or not you want to continue with law school...well it sounds like you don't really want to, so if you can eat the cost of one year, I'd say do it.

Keep in mind that a JD from HYS will go very far, wherever you wind up. But if you don't think you need it (and it sounds like you don't really want it) then there's no reason to continue with it.

I also think you should at least finish the summer job, for professional reasons (you never know if they'll come up as a reference or something). There might not be that much time in the summer left after you hear back from the job, get started and all that. But if you get the job offer, decide you really want it, and need to start right away, I don't think leaving the job would be the end of the world. As long as you're not a jerk about it.
Judging by the tone of your post, it seems like dropping out and working is what you really want to do. Walking away from HYS is certainly a tough call, but if you aren't going to like law, then maybe it's the right call.
Maybe before you decide, talk to older students/lawyers and see if anyone else was in a similar position as you, like they didn't find 1L or their first job that interesting but later found a niche and liked it... along those lines. I find that most practicing attorneys I've talked to about law school/careers are pretty candid and honest about it (unlike career services of a school).

Finish the summer if at all possible, but definitely drop out of school. You have a legit opportunity to pursue a career that you know you will enjoy. Take the loss on 1L and move on with your life.

Finish summer, leave for job if you will be more happy in short and LONG run