First time I saw mid Lulu in a competitive setting she was played by Zamphira. He used a full MRpen build, and I'd like to clarify the strengths of weaknesses of this build. Well, mostly weaknesses.
First, what strengths do the MRpen build have in general. The strength of the MRpen builds are
A) Scales with base damage of spells instead of only AP ratios
B) Is really strong against very low MR targets
Looking at Lulu reveals that her offensive AP ratios are horrid - 50% on Q, 40% on E, and up to 15% per passive proc. So if we were to insist on only building for offensive capabilities, it would look like MRpen would be the way to go. But then look at her base damages. These are in fact also absolutely terrible. No damage on ult, her E is often best used defensively, and W only scales with CDR/AP.
If you really were to make the best of the MRpen build, you'd have to go for low MR targets, so you'd be diving, playing assassin. It just feels like Lulu is not the best for this role.
I've been a sucker for Lichbane since I first considered the math involved. For raw single target damage output, Lichbane is sometimes beat as a first item, rarely beat as a second, and practically never as a third item. It is restricted to auto attacks though, with all the downsides that follow.
But Lulu's auto attacks are already good, she should be trying to weave them in between spells anyway, and she sorely needs extra output to fulfill her role and warrant the farm given to her mid.
Consider that Lichbane adds 150 damage to Glitterlance and Deathcap adds 81, both from 0 AP. With Lichbane, every 1.3 AP adds another damage, Deathcap needs 5.7 AP to add another damage. And that's not even considering that your W and R which would otherwise not deal damage also trigger Lichbane.
I very rarely see Lulu's E used defensively and it puzzles me. It's incredibly more efficient when used defensively. Firstly it scales better with AP, but the most important thing is target mitigation. When used offensively, you have to get through their MR. When used defensively, they have to get through the target's mitigation.
Lets have a look at basic low mitigation situation with low AP, which favors the damage mode the most. Both targets have 30 armor and MR and you have 0 AP.
The result is that shielding is 69% more effective, or the equivalent of a 138 AP difference. Now that was a very early game example. Lets say you have 100 ap and the armor/mr is up to 50. You're now nuking for 80 effective HP or shielding for 210 effective HP, an increase of 162% effectiveness or the equivalent of 488 ap. So just by shielding instead of nuking you've effectively added 6 large rods to your inventory.
And it gets a whole lot worse. Lets say you're helping your a bruiser take down an AD carry. The carry has 50 armor and MR, the bruiser has 250 armor reduced to 150 by ArP, and you have 400 AP. The result is a difference in effective HP contributed of 400%. The equivalent of 2400 AP.
And then there's the benefit of giving Pix to a target with higher attack speed (or better attack application, such as the bruiser that's diving carries). After around 3 additional attacks, the damage from shielding surpasses that of directly nuking.
There are obviously many scenarios where the shield won't be used or the damage dealt will still be worth more than the damage mitigated or the position of Pix is more valuable on the enemy. Just remember to consider how much the health of your potential targets is worth. While it may produce a bigger EHP swing to buff your tank, the health of your diving assassin / dived carry is probably worth enough more that it's better to shield them. But in general, when in doubt, shield. Especially if you're my support in botlane.