If it's 120 Hz it can't be that old and as such is less likely to have a high amount of input latency. I'd put up with some input latency to have 120 Hz over 85.. ugh. Plus the LCD is likely to have a sharper/better picture than his old and weak CRT. Good CRT would be another story.
What model are you using Tsubakii?
120Hz needs 8.333ms to refresh, 85Hz refreshes in 11.765ms. That's a difference of 3.4ms. Between input lag and pixel response time, it has to be in favour of a CRT. Given that some expensive gaming LCDs on the market give a response of around that much for input lag alone, I think it's safe to say that if it's noticeably blurry for him and not a good LCD screen he would be way better off with a CRT. I don't understand what you mean by "old and weak CRT" (?). The choice is obvious, in that screen he's getting blurry and slow images, on the CRT they are sharp, it's the same way for me. It's well known that the Hz, whether it's 120Hz, 85Hz, or 60Hz, isn't the main bottleneck people face with monitors. Can't believe you're talking about "sharper" with LCD screens when he just said that it's blurry on that (think when there is movement), no offence. I feel a bit sick/disoriented after watching fast movement on many LCD screens, loads of ghosting. The CRT screens have the highest contrast and best displays, that's why they're still used a lot in high end photography and professional gaming - the only reason they use LCD screens at those events is due to logistics, and it's fair if everyone is on the same level.