I often see Mordekaisers rush Sorcerer's Shoes? Does it have something to do with his shield or do they need it just so they can survive the laning phase?
Mordekaiser is typically built AP. Usually, APs build one of two boots: Ionian Boots of Lucidity or Sorceror's Shoes.
Mordekaiser is also a melee champion, and the early movement speed helps him get to his enemy faster without being kited too much.
Not to mention, his starting movement speed is only 315. Also, the boots give mPen which buffs all of his spells. Finally, especially if the enemy doesn't have boots, Mordekaiser can run up to him, blast Mace of Spades, Creeping Death, and Siphon in his face and run away without taking much damage.
Normally I don't play Mordekaiser that much, but it would be logical for him to rush for the boots.
First of all, it allows him to hit harder, hence filling his shield faster.
Second, he has 315 movement speed, and the boots allow him to easier escape ganks, since his only escape mechanism would be flash.
Finally, as a melee caster (assuming he goes mid), boots allow him to faster move to minions and receive even less harass from the other mid than normally (less poking at his shield).
I believe the logic behind purchasing these boots comes from Mordekaiser's passive, Iron Man. The passive states: "35% of the damage dealt from abilities is converted into a temporary absorption shield." Since the magic penetration from Sorcerer's Shoes allow your abilities to deal more damage and thus generate more shield. Additionally, the same principle applies to the Spell Vamp from Hextech Revolver (which is another core item on Mordekaiser); the life gained is based on the damage dealt.
In summary, having Sorcerer's Shoes allows you generate more shield and regenerate more life with Spell-Vamp from your abilities.