Just bough Lee Sin yesterday ..... and here is how I go about him...
I do the standard jungle clear and skill order as recommended by most lee sin guide(red start and e skill followed by w and then q). When I go to gank , the problem comes ...
If I just walk up to my opponent to e or w to my ally so as to e him and then follow up with q, my lanemate and me dont have time to finish off the enemy and he gets away with very little health ... I also know how to wardjump fairly well (practice in customs with jax) ... in post 6 ganks , i q the enemy, walk behind after hitting e and ult him back ..... in teamfights, i either stay and ult away the most threatening enemy to my adc or i try to q the enemy adc and ult him out of position.

Basically , how do i ensure kills as a new lee sin during my ganks?

Make sure you get two AA inbetween your spells to not run out of energy and to get full use of your passive. You'd be surprised how much more damage output he has if it is used to the potential. If you are doing this, then by what your saying, I'm not sure if you can do anything else.

While AA weaving is important, there isn't a set number of AA's you should have per spell cast. It's more of a feeling around for the right pace. If your lanemate has any sort of cc, you typically want them to pop it as you're going in so that you can close on them without them sprinting back to their tower. Remember that while the second half of your q is a gap closer, it also functions like an execute (8% of missing health added in damage). With that in mind, you can w to a minion, e for the slow, q, step around the champ, kick them in the face, q back to them for more burst. Otherwise, you usually just lead with your q and attempt to burst them down with your lanemate's help.

also when i play as lee (bought him new myself but i find this with other junglers that only have a slow) the early ganks tend to not grant kills as much.....depending on your jungle. I have found that going exhaust smite lee works well on ganks...with this you have to be more careful of your own positioning though since you dont have flash/ghost. you have to use your w to get out.

just find your groove and you will be golden

Initiate ganks using your w on your ally when the opponent engages them. Never q first save it for as they are trying to leave in case they flash away you can follow it up. Always carry wards it's your escape with w. cripple strike walk in front of the opponent use your r followed by your q right after. Get your q shots really well and you will be a god.