Oh, I don't know about the last part...I was running out of mana pretty regularly till I built a Tear->Archangel.
In a lot of ways, she's in the LeBlanc/Orianna/Ahri mold of casters with low cooldowns across the board. Lulu doesn't have the chain-casting as explicitly as Ahri or LeBlanc (or Brand) does, but she can still reel off a string of W+E+Q and wreck your shit.
But once you get mana regen up to a good level, you can kinda just hang out and get enough mana to toss a Q every 6 seconds or so, at least enough to fight a delaying action in lane till your partner gets back to hold the line so you can B.
I think what I like about Lulu is that she takes the rapidcaster concept of the aforementioned characters and weds that to a pretty awesome utility support, so that if you're paired with a DPS melee type character, you're an unholy pair of badasses.
Q enemy (for slow) + W ally (for speed boost) + E enemy (dmg + reveal) = You're not getting away this time, Teemo/Shaco/Wukong.
Q enemy (slow) + W enemy (for silence) + E self (shield) = You can't catch me, I'm the Purplebread Girl!
It's that versatility/adaptability that's so damn dangerous. Downsides: no area CC (other than the ult's minor knockback effect), less single-target damage compared to an assassin like Ahri, or a burst caster like Veigar, only one AoE damage.
If you pair her with an AoE melee like Alistar or Amumu....*shudder*.