I'm wondering if lifesteal works on Brands autoattacks, I assume it does but AP carry is very new to me.

Lifesteal works on all champion's auto attacks since they deal physical damage, while spell vamp only works on abilities that deal magical damage.

If you play brand AP (the normal way) then it is not advizeble to have lifesteal on him, because he deals dmg with his abilities and just a little with auto attacks.

So if you want to have the same effect as lifesteal on AD champions, you have to buy spell vamp items.

Hextech is a good option really cheap too

For a champion like Brand, I would advise items that give alot of ability power such as Rabadon's Deathcap, Rod of the Ages, Void Staff and Zhonya's Hourglass

Lifesteal is a percentage stat which returns a certain percentage of your basic attacks to you as health (no extra damage is dealt)

Spell Vamp is the mage version of Lifesteal because if you have say, 20% Spell Vamp, 20% of your magic damage is returned as health, the champions who use ability power and spell vamp are Cassiopeia, Ryze and Vladimir as Spell Vamp is more needed for sustain because the other mages, Brand Veigar Lux Morgana Anivia etc all are "Burst" mages as they do massive damage really quickly and Cassiopeia, Ryze and Vladimir is "sustained dps" who do damage at a conastant rate so spell vamp is more usable for them as the healing is coming in more consistantly.

Hope this helped!