Apparently a young Ludwig van Beethoven did meet Mozart once in his lifetime before he died. Like most things in history, it can't be 100% accurately verified, but the encounter goes something like this:
'Beethoven made his appearance in Vienna as a youthful musician of promise in the spring of 1787, but was only able to remain there a short time; he was introduced to Mozart, and played to him at his request. Mozart, considering the piece he performed to be a studied show-piece, was somewhat cold in his expressions of admiration. Beethoven, noticing this, begged for a theme for improvisation, and, inspired by the presence of the master he revered so highly, played in such a manner as gradually to engross Mozart's whole attention; turning quietly to the bystanders, he said emphatically, "Mark that young man; he will make himself a name in the world!"'