Honestly while these are some good suggestions, they aren't really addressing the true problem with Lee Sin. See, the issue with a Lee Sin is that while he falls off during the late game, from a numerical standpoint he has an unfair advantage over pretty much every other jungler who builds the same items as him at the same time as him.
Say, just for the sake of simplicity, that you have a Lee Sin and a Shyvana. Ignoring their first items, since a Shyv is probably going to build Devourer's while Lee Sin builds a Warrior's, focus on what they get next. The Shyvana is planning to play as an off tank, which arguably works better for her in the late game. She knows she won't need mass single target damage so instead of getting a BotRK early on she instead builds a Hydra, as does Lee Sin.
Breaking things down to their scalings on their damage abilities reveals why Lee Sin poses an oppressive amount of force in the early game and an unfair advantage in the midgame:
From the same 75 AD that both have built from a Hydra, Lee Sin's abilities are dealing far more damage than Shyvana's, even assuming that you stand in her W for it's full duration while taking the sustained damage from her E marks while she's AAing or Qing you. Eventually she might do the same damage as a full Lee Sin combo, but she isn't going to do it nearly as fast, and she isn't going to do it with both the mobility and the utility that Lee Sin brings. Because of this, Lee Sin's ganking harder, and his high mobility allows him to put pressure on lanes a lot faster than a Shyvana, or pretty much any jungler early on, will be capable of doing.
All the same, Shyvana starts getting fed off lanes where Lee Sin isn't. Because their top laner has decided to build as a straight tank, perhaps it was a damage focused Nasus or whatever before this, just bear with me for the sake of the example, and Shyvana's up by a few kills she figures it's safe to build another damage item. So while she's working on a BotRK, Lee Sin builds himself a Randuin's Omen. As we enter the mid game of this little matchup, Shyvana is now starting to deal comparable damage off of her kit to a Lee Sin in a smaller amount of time. Within a few seconds she can eat someone alive, and keep them within range between the BotRK active and her W's MS boost. However, Lee Sin can still kill them much faster, and with much more ease, because the scalings on his abilities are so high that his damage has remained consistent from his early game while he has more mobility options than Shyvana. As Shyvana is only just reaching somewhere near the sheer damage output that Lee Sin can do off of one item with her two items, Lee Sin has also built a defensive item. And herein lies the other issue with Lee Sin's kit aside from his insane early damage:
With few damage items, a Lee Sin can build tanky after that and still keep his damage completely relevant during the mid game due to his scalings. Because he is getting so much more than Shyvana is from just the 75 AD granted by the Hydra, as Shyvana is only just starting to equal his damage he's getting the edge on her in another department: defenses. Lee Sin can now unload on someone and even if they can withstand his initial burst, he can survive long enough to go in soon afterwards because of his low cooldowns. So with only two items built on either side, Shyvana is only barely reaching the same sort of kill potential while Lee Sin is much more durable.
Shyvana begins playing catchup, building her own Randuin's Omen while Lee Sin builds some MR with a Spirit Visage, or perhaps a Banshee's Veil. Shyvana matches this afterwards by building a Maw of Malmortius while Lee Sin builds a Warmog's Armor.
Going into the end of the mid game, nearing the late game or going into it, the matchup is now this:
The Hydra, BotRK, and Maw are giving Shyvana a definite edge in damage, in terms of armor the two are comparable, with the advantage likely going to Shyvana due to her passive, especially in dragon form, and in terms of MR the two are about even, again with some small advantage going to Shyvana due to her passive and dragon form. However, with the same number of items Lee Sin also has a considerable amount more health. And had Shyvana built a Banshee's Veil or a Spirit Visage to give her more tank stats, she would still only be dealing comparable damage to the Lee Sin instead of outdoing him in that department, so he would still have more health either way, even if their MR were similar.
While Shyvana is lstill quite capable of absorbing damage in dragon form, she's having to give up some of her durability potential in favor of damage in order to get some sort of a lead on the Lee Sin in at least one department. If she does not build more damage, she is instead allowing herself to tie him in two, maybe three departments (damage, armor, and MR) while giving him the advantage in health. So either she accepts being not as durable during teamfights by not building more health, or she accepts only just keeping even with Lee Sin but has to hope her allies can deal enough damage to compensate for what she's lacking.
This is how Lee Sin stays relevant early and mid game. A Lee Sin can build a single high AD damage item and retain his strong power curve for the next 20 to 30 minutes of a match. It isn't until the other team has built up their defenses enough to stop him being able to eat them alive, meanwhile likely giving up on damage themselves doing so and making it harder to fight against a team building heavy damage to push the advantage Lee Sin has given them, that a Lee Sin will fall off. He relies heavily on small skirmishes as his skillshot can be difficult to land on the correct target during a teamfight, and no matter who you are diving into 5 enemies is never a good idea.
Except possibly Rammus, but he's the exception and we love him for it.
This is where the Shyvana, who has comparable or possibly more damage, depending on how she built, while having similar defenses if a few hundred less health, will appear to be outscaling the Lee Sin. She has many more options to handle a teamfight, considerable AoE damage above and beyond Lee Sin, and can actively engage a fight because, let's be honest, there's nothing quite like the feeling of dragon forming into 5 enemies with your burnout active and going ham with fire breath and cleaves. However, this appearance of being outscaled is entirely artificial.
Due to his high scalings, if a Lee Sin and a Shyvana were to have the exact same builds, the Lee Sin would be doing MUCH more damage. If both Lee Sin and Shyvana were to build Hydra, BotRK, Maw of Malmortius, Bloodthirster, and Mercurial Scmitar (I'm aware that no one would use this unless they were likely just dicking around, but it's just an example for the numbers), both of them are sitting on oh, about 350-ish damage from items, and they both have somewhere around 16-1800 health, I don't know exactly how much either of them would have if not building any health items. So we'll just say 2000 for the sake of ease.
Lee Sin and Shyvana meet in top lane. Shyvana readies, turning on her W and rushing him, possibly even ulting over him with it active to give herself the bonus resistance. Her Q will deal, assuming it's maxed at this point, is essentially two full autos at one time. So she autos and then Qs, her most simple damage combo, dealing roughly 900 damage after the armor reductions, while her burnout is dealing an additional 140ish damage between it's base damage and it's AD scaling, in the one second it takes her to hit her auto and her Q while he's standing in it. So all in all, in that one second of the fight Shyvana has dealt roundabout to 1050ish damage or so. If she had tagged him with her E, that's 6% of his maximum health, from the three procs off of her one auto and two Q hits. Assuming he has 2000 health, that's dealing 120 additional damage. So she's dealing about 1200 damage altogether in a single second of combat, not accounting for a Hydra active or a BotRK active as that isn't inherent to her kit, and he would have access to the same for his own combo.
Lee Sin, on the other hand Qs her once, and as she lands on him he uses both of his autos that are hitting faster from his passive. So that's two autos, so about 600 damage, and then a Q dealing 170 base damage and 90% of his bonus AD, so about 320 damage. So off of one spell cast and two autos he's dealt about 1000 damage. At this point Shyvana has used all of her available spells and is reduced to using auto attacks for the next four seconds or so while her Q comes back up. So while she's hitting him for another 300 damage for an auto about once a second, and another 140 damage per second from her W being on for another second, she's brought the total damage done in two seconds to about 1500 damage. 1540 from the E mark proccing.
Lee Sin hits his E once, dealing 200 base damage and 350 bonus damage, and his next two autos happen in the same amount of time as Shyvana takes to hit one and get another ready. So in the same two seconds of combat that Shyvana has dealt 1500ish damage to Lee Sin, the Lee has added another 600ish to the 1000 he dealt the moment before off of just an ability cast, bringing him up to 1600ish, and his next two autos go through during the time Shyv tags him with one.
In two seconds of combat, an equally built Lee Sin has dealt 2200ish damage while the Shyvana has dealt only about 1500 damage. And even if the fight were to last another second, bringing Shyvana to the point where she might be able to kill him due to adding on another 140 magic damage from W, another 300 damage from an auto attack, and another 40 damage from the E proc (making her total damage done about 1980ish damage), Lee Sin still has his ult. He hits R, and deals a flat 600 damage plus another 700 from the scaling. Three seconds of combat, two very different totals. Shyvana clocks in at about 2000ish, while Lee Sin is weighing in with a total of 3500 damage.
Lee Sin does not actually get outscaled in the late game. He simply stops building damage so appears to be outscaled when he actually has superior damage scaling.