As with anything, it probably depends on what factors you are looking at to make a determination of what constitutes a "successful" attorney. I'll take my two brothers, both attorneys, as examples.
One did decent on the LSAT (170 range) and, after a stint in "big law", decided to go the solo route. His goal was never "money-oriented" and his practice is focused on what he loves doing, which he describes as "helping people." He still makes decent money, around $120k/yr and has flexible hours. Now, did his fabulous LSAT score matter? I think most would probably say no.
My other brother didn't have a great LSAT score, but did well in a T2 law school and still practices in a "big law" shop. He's commented many times that one of his weaknesses, even 5 years in, despite his other formidable strengths that have allowed him to propser, is the fact that he sometimes gets caught up and takes longer to analyze statutes. For him, this mostly arises when he's working on securities matters and he's often said that if it were the "older brother" reading the same statute, the older brother would probably take half the time because he does better with logical reasoning, as evidenced by his LSAT score. So, from his perspective, although he does not believe his LSAT score has hampered his career in the "big picture" he admittedly feels like he is at a disadvantage for certain areas that require an immense amount of logical thinking.
LSAT scores might also matter more if they were actually closely correlated to law school success. I understand that they're "supposed" to be, but once you figure out the law school "game" most people can probably excel, regardless of LSAT scores (for the most part). Frankly, I think that if you're smart enough to cut through the typical law school BS and understand what to focus on to be in the top of your class, then "big picture," you'll be in a good position to succeed. But, if you can't make it in law school, regardless of LSAT score, you may have a more difficult time succeeding as an attorney. Exceptions always exist and my points above admittedly fall prey to one's mental bias to use specific anecdotes to form opinions even with more general, statistically sound evidence available, but that's my two cents.
I'll also note I've heard plenty of stories of brilliant attorneys who aced the LSAT and law school and end up in top law firms, but don't end up "succeeding" in the big picture because their personalities make business generation and client service difficult...they can end up as the attorneys who do all the work but never get client face time. Again, all comes back to what your yardstick is in measuring "success"