By now, you have probably made the switch to management consulting. And if not, it is fine. Life, sometimes, takes us through different routes. If you haven't, and still interested in it, this might help. Perhaps, all you need is the perspective shift.
Now, this response is based off on what I heard from an Ex-Mckinsey Partner, Micheal Boricki (now works with FirmsConsulting, helping people like you make the carrier switch from law to management consulting in MBBs).
I found his answer very exhaustive and I am going to paraphrase it here:
The short answer to your question is this: “If you are an amazing lawyer, it is probably easier than you think.”
Who presides over every single one of the world’s business conflicts? Judges. And do they hold an MBA or studied business? No. They are lawyers. As a person with a civil engineering background, I find it interesting that someone like you without a business degree is the go-to-person in massive and large business decisions (take for instance the recent T-Mobile and Sprint Merger ruling).
If we accept their ruling, then there must be a different reason (that has nothing to do with our initial bias that this person's lack of a background in business is important in evaluating their credibility). The answer is in the way lawyers think!
And the way they think is highly prized at Mckinsey, BCG, Bain, et al! They call it Analytical Thinking. And Lawyers are the one group of people with a high level of analytical thinking capabilities. If you can show that you are an analytical thinker, every other skill you need to learn will come naturally to you as you prepare for your case interviews.
You should know that there is a difference between analytical thinking and quantitative thinking. Many people often confuse the two together. That you are good with math shows that you are good quantitatively but does not necessarily mean you have analytical thinking capabilities, else Mckinsey will be filled with Engineers, Accountants, and Mathematicians. That is not the case, consulting firms are filled with analytical thinkers, a group every good lawyer belongs to.
Don’t undersell yourself. You have what consulting firms crave for!
If you prefer to listen directly to the Ex-Mckinsey Partner who helped me understand this, check out this podcast on youtube: Career advice: Is art or law background worthless to management consulting?