Jim Lee, who redesigned the X-Men costumes, logos, and equipment around 1991 was a Trek fan. So the similarity between chairs is likely deliberate. However, Lee's Professor X wheelchair wasn't supposed to be a hover chair. Rather it road around on a giant ball.
I've been rereading his X-Men work, and LCARS definitely pops up here and there.
I seem to remember X-Men watching Star Trek on TV ia couple of times.