You're right. In pro play, he's not situational because LCS junglers only pick early game champions. He is, however, always valued below multiple other junglers and is generally only picked when champions like Rek'sai, Elise, Kindred, Nidalee, Graves, etc. are unavailable. Point is, Lee is, and has been a last resort pick for pro junglers except in situations where that particular jungler is exceptionally good at him, such as C9 Rush or OG Amazing. Regardless of how strong or weak Lee is, he's been incredibly popular for ages and provides the early strength that pro teams require, so literally every pro jungler is at least a competent Lee Sin at the very minimum. That's why he sees play. It's the same reason Lucian still saw considerable play last season despite having bottom tier statistics: Every pro adc can play Lucian and he has the skillset you want from an adc in competitive play.
Take away the competitive environment however and both of those champions were very mediocre last season. Lee Sin still is. He fits the skill set pro players want and is thus desirable enough to pick at that level even when weak. But he's garbage in Solo Q and has been since early season 4. His dueling power is a mere shadow of it's former self. He's less mobile than he was before. He's less tanky than he was before. His sustain in the jungle is weaker than it was before. Counterjungling as a whole is far weaker than it was before, lessening one of his greatest strengths. He's not even viable outside of the jungle anymore except as a cheese pick. Actually winning games with Lee is a serious struggle and even Lee players recognize that you play Lee more because he's fun than because he's actually good. I know I don't pick him when I'm going full tryhard mode. If I'm trying my hardest to win, I'm picking Sejuani, Shyvana, or Pantheon. All of those champions are stronger, easier, and more reliable than Lee is. But damn it all, Lee is more fun to play.
I really suggest you try him out for yourself. I know you haven't played him before, or at least haven't played him in years, even in a normal game. You've already shown a willingness to have your mind changed before when we discussed Sejuani. If you're willing to test your assumptions on a champion you already play, then you should be even more willing to test your assumptions about a champion you don't play.