Ok, a few things,
Firstly drop the LSG, as they're an underpar unit who are less efficient than the other Core choices. Drop them and either get another unit of archers, or some more Silver Helms. If, by doing this, you can get a unit of 15 Helms, that's fine, but, if not, split the helms up into two units of 5/6 with just a musician in each.
20 White Lions really aren't going to do all that much on their own, so I'd drop them and get a
BSB (vitally important), beef up your Phoenix Guard a little more (to at least 25), two Eagles (which are really useful in lists where you have hard hitting units on the charge), and a talisman for your Archmage, if there's any points remaining.
Next, on your characters, you'll want to run the Lore of Shadow on your Lvl4, and keep him nice and safe in the archers. I wouldn't go with High Magic on your Lvl2, as you can, if you wish, give Khaine's ring to the
BSB, stick him in the Phoenix Guard, and use that to boost their Ward Save. Lvl1 Beasts would probably be the most effective use of your hero Mage, but Metal would work well too.
Finally, I find Dragon Princes much more effective than Lion Chariots, but if you want to include the chariots, then that's fine.
Hope this helps, if you have any more questions, feel free to ask!