Composer Juozas Naujalis founded a music school in 1919 in Kaunas.

On 31 August 2021, the construction of a campus in Olandų Street (Antakalnis) began.

The Academy strives to "develop international cooperation and integration into the European and global academic community, to support and facilitate student and teacher exchange, and to ensure high-quality standards in higher education in the arts."

The LMTA has bilateral agreements with 72 partner institutions across Europe in the Socrates programme.

Other bilateral or multilateral agreements have been signed with the Belarusian State Academy of Music, Moscow's Tchaikovsky Conservatory and its Slavic Traditional Music School, the Rimsky-Korsakov Saint Petersburg State Conservatory, and the University of Kansas.