This post is in case others with the same question are reading this board. I'm not getting into the personalities, but this question was a question I had to work through to go LSR racing.
The minimum cage requirements on LSR will meet 8.50 NHRA requirements, but not necessarily vise versa, so if you are building a "dual use" racer, you need to read the SCTA book first, then the NHRA second. Wall thickness is heavier for SCTA, and you need head restraints. You should also make provisions for a HANS device. Mitch at Mitch Fabrications built our LSR cage, and while it still at his shop, we had both SCTA and NHRA guys check it over, then had the NHRA guy cert it ($110?). SCTA doesn't make you pay to cert your cage, but NHRA does.
We attended our first drag race last weekend at Famoso since we upgraded the cage, and they liked it. We didn't go as fast as we wanted, but that's how it always is.