Short answers, pulled from the story.
The Battle of Lützen occurred because European powers sought to remove Napoleon from power after his failed Russian campaign. Prussia secretly allied with Russia on the 27th of February and declared war on France on the 6th of March.
Napoleon could only muster 145,000 men for the battle because the XII corps and Wurtemberg division remained two days' march away. He raised approximately 200,000 men through mass conscription but these reinforcements arrived largely inexperienced by late March.
The battle took place on the 2nd of May 1813 when Napoleon reached Markranstädt with Lauriston's V Corps. Nightfall brought the engagement to an inconclusive end despite Napoleon controlling Lützen and the field afterward.
General Blücher led the Prussian corps while General Wittgenstein commanded the Russian forces. Gerhard von Scharnhorst served as Wittgenstein's Chief of Staff until he died from a fatal infection following wounds sustained in the fighting.
Napoleon lost 19,655 men including 2,757 killed and 16,898 wounded during the engagement. One of his marshals died in the fighting while casualties may have been much higher than recorded figures suggest.