Do you have armor seals and jungle based masteries? I play Lee Sin sometimes, and yes, absolutely the S5 jungle is harder for him and most all other junglers, but as long as you have your masteries and things set right and you use your w as often as possible, you should be alright. I recommend starting your E, (Tempest/Cripple) for damage to all the minions in the group for your buff. And then probably level your W at level 2 so you can heal up, your E will trigger some of the lifesteal from your second W active, as well as giving you the two faster autos with your passive.
And if nothing else, make sure you use your passive AS MUCH AS POSSIBLE, as it really determines your clear speed and ability to kill literally anything. And it takes a reasonable amount of time to find your most efficient jungle path and making sure you really get your abilities. If you really feel strong, for max lifesteal from a smite, use your W, and make it so the second active is going for your increased lifesteal, and hit a sonic wave on your monster/buff/dragon/baron etc, and smite it just a little early, as your second Q hit increases damage based on missing health % on enemies. That will get you the most health back from hitting the same 2 keys versus hitting your second Q and smiting for the execute. Just something my Plat friend taught me when he half mained Lee Sin jungle in Season 4.