I'm a major fan of LK and his lore, but let's just be realistic here.
In a 1v1 there would be no chance LK could win against Azshara, not before her transformation or after. We don't know if the well's destruction made her weaker or more powerful, but considering that she drowned/close to drowned in the WoE I'm going to to assume the latter. If her proximity/connection to the well is the source of her power, I'd dare say she more or less became one with it as N'zoth made her into NagAzshara.
Now let's take into consideration their styles of combat. LK is primarily melee, he does use magic, but I'd say his magic would be vastly inferior to Azshara's, so I believe without melee he'd be fodder. With melee, range becomes the new problem and I simply don't see him getting in to hit the execution, not if her power is so immense as I think we're led to believe.
With all that in mind, I simply have to say Azshara.
Now Scourge vs. Azshara + Army. I'm actually not sure. If it's her nagas only then definitely LK, but if she has the OG forces with her I think it becomes another win for Azshara.
Azshara + Burning Legion would also smash LK, everyone who played WC3 knows what a long con they had to play in order to get a shot at freedom.