Split Earth at level 1 because it prevents or seals first blood attempts you might encounter. Then, we max Lightning Storm first because it is our laning spell; maxing Split Earth alongside it.
Diabolic Edict is taken later because 1. Lightning Storm has a potential AoE of 1350, way more than Edict's 500; 2. early game is about laning, and Diabolic Edict is weak in a lane due to creeps; and 3. Leshrac's HP makes it dangerous for him to get into that range, unless if he will follow up an ally disable with Split Earth.
Pulse Nova is taken at either 10/11/16 or 13/14/16 because Leshrac's mana pool is still small at that time. Many will prefer to level it at 13/14/16 because by that time, you should be on your way to your Bloodstone, which makes it possible for you to handle 4 active spells while letting Pulse Nova last for a decent duration.
An alternative skill build for fast tower sieges (and quicker kills) would be replacing Lightning Storm with an earlier Diabolic Edict. This poses more risk than the conventional build and should only be used on coordinated games.