if not for BYU's greatest basketball coach (hall of fame, fundamentally changed the game, national championship, many many All Americans and pros, etc.) Stan Watts, we would never have had the Lavell years. Stan Watts became the AD toward the end of his time as basketball coach and he's the one who hired Lavell.
I'm not saying BYU is a basketball first school (they once were, but that changed a long time ago now). Obviously the fanbase is football first. That's fine. But football isn't what it is at BYU without basketball and those who came to BYU for basketball first; because they were in place to then support football and make football what it became under Lavell.
Basketball's early success also showed church and university leaders that a successful athletics department was really good PR for BYU and by association, the church. That's why they were willing to invest in football.