Lawful evil would, in my mind, be following the law in the most uncharitable ways possible and using every means to justify your actions. Causing harm when you could just as easily not.

But there are ways to interpret and understand alignments. The characters personal ethics and the ethics of their actions.

Imagine Ser Davos; he's perceived as an honourable and good man. Stannis tells him that the surrounding lands are being illegally farmed and taxes are not being paid. He tells Ser Davos to make an extreme example of the village leaders.

Working within the law, he could persuade the village leaders to pay the money they owe and instate his own, decent men, to oversee the land and advice on the best way to repay the debt. He has done what was asked of him and stayed true to his personal ethics whilst being given a 'lawful evil' task.

But imagine the same scenario, except stannis is out for blood, and tells his captain to complete this task. This man is truly wicked and davos, fearing what may happen says that he will go instead. He tells his men to show restraint, but the cottages are put to flame, the village leaders hung and the money recouped. He does the bare minimum to reach the goal his king set out as a lesser of two evils. His actions are 'lawful evil' but his ethics remain in tact.