Hi there! I'm going to try addressing some of your points; pardon me if I seem to be a bit disorganized.
IIRC, Lee has been emphasized by Rioters as an early-game gambit champion; he offers a lot of power at level one, but he falls off late game. The nerfs to him in recent patches have gone a long way towards shaping him to fit that role better; if he's having trouble late game, that's what Riot wants.
If you spam your spells while jungling, of course Lee's going to run low. That's why his passive exists; by spacing out your spells, it's pretty easy to stay with medium to high energy as you run from camp to camp.
At early levels, Lee actually does a ton of damage; have you tried invading on an enemy jungler? A pretty cheesy start is to take your buff, then go and wait for the enemy jungler at his second buff. Level W first, take a buff, level Q, then run straight towards the enemy buff that the enemy hasn't taken yet. If you play it right, you can win the buff and even kill the enemy jungler.
I didn't exactly like the nerfs to his W, but I find that it's fine to sustain in the jungle if you have the right runes and remember to activate W. Though I'm running life steal quints, so that might be a factor... either way, his W seems fine to me. I mean, J4 can only dash to his flag. Lee can dash to wards, teammates, and minions.
In late game, he does fall off, and I try and compensate usually by going more utility oriented. I don't try to get kills on Lee late game; it's more about getting in and getting a good kick off, IMHO. Building those items you mentioned is actually a pretty good idea for that reason.