Spain were also champions in 2009 and 2011.
Pau Gasol was chosen as Most Valuable Player, with 25 points and 12 rebounds.
"The basis and the key to success is that each one of us has done our part in order to win this gold," Gasol told newspaper La Informacion.
"There were moments where [Lithuania] were scoring in the game, but fortunately we had more experienced players than them and he set a better pace from the beginning," the Chicago Bulls forward added.
King Felipe VI presented the medals to the players as their fans cheered them on.
This was the second consecutive silver for Lithuania after the team lost to France in the 2013 final.
France beat Serbia for the bronze for this year's EuroBasket, also on Sunday.
Spain, Lithuania, France and Serbia have all won slots in next year's Olympics in Rio de Janeiro.
Spain took home a silver in the last two Olympic games for basketball.