A paladin's divine smite says (PHB. 85), "...when you hit a creature with a melee weapon attack...", which I'm seeing two ways to interpret.
"A melee attack with a weapon", so as long as it's a melee attack and you're using a weapon smite away.
"An attack with a melee weapon", is where things get odd. Under (PHB. 149), "Simple Melee Weapons", includes spears which have the Thrown property. Thrown states (PHB. 147), "...you can throw the weapon to make a ranged attack. If the weapon is a melee weapon...", so even while being thrown it is still a, "melee weapon"
Since it would be easy to house rule this (Rule of Cool: Smiting with a spear sounds neat) I'd like an answer that either references word of god or provides a convincing argument that this type of reading applied to other parts of the rules results in absurdities.