finance vs law in lse

Would it be better to study finance, management or law at lse if im looking for a good work-life balance or at least an enjoyable job?

Management

There's some assumptions here you are making, mainly being that studying any one of those degrees means going into one career path and sticking with that. Finance and Management can open up very broad paths, from accounting, finance, consulting, to retail, and you migrating from path to path depends on you and how determined you are in doing so. Choosing one of these degrees (except for law, because realistically there's no easy exit from that) does not confine you in any major way. I know people that do engineering that are now in bulge bracket banks, and I know management majors that are now in FAANG/Big Tech.
However, the majors you've listed are almost anthesis of "work-life balance". Prepare to be worked like a dog in areas such as IB (60-70 hours/week), consulting (50-70), and law (50-70+), at least until you get to a pretty senior position. Now, whether these jobs are enjoyable is entirely up to you. If you enjoy the eventual work that comes with some of these career paths, then that's great. But know that none of these high-paying jobs come for free, and your time is the always the cost that comes with that.