Harass everything that moves. At level one, farm aggressively until the opponent gets in range or your E. Then, use your E on them and auto twice to proc electrocute. Keep doing this until you hit lvl 2. Once you get your Q, you can replace one of your autos with it, allowing you to proc electrocute easier. However, if your opponent is an assassin, poke at them safely until you hit lvl 3, which then you can W them if they dare dive you. Remember, use your autos. In my experience, roaming has not been really beneficial until you hit lvl 6.
In the late game, Lulu is still really good since she has a ton of utility. However, if you played Lulu correctly, you should not have to rely on your utility. You should have massive attack speed with a ton of burst damage from your abilities as well.