This is a big stretch, but "mazlis" means lucky in Hungarian...perhaps shortened to the catchier diminutive "mazzy"...lucky star? Maybe someone in the band has Hungarian ancestry? Just a thought.
if you mean "lithium" its evanescence Nirvana also has a song entitled "Lithium" that was released in 1992.
Dead or Alive Deadeye Dick Grateful DeadTheory of a Dead man
Lemonade Mouth Meat Loaf (not really a band, more of a musician)
Zach
Their drummer kept writing the name on the back of his textbooks in high school.