In 1931 he moved to the Franz Liszt Academy of Music, located in Budapest, studying under Ernst von Dohnányi.

It was during this time, Rajter was invited to conduct several European orchestras, and premiered works of numerous Hungarian composers, including the Symphonic Minuets by Ernő Dohnányi.

[4] In the Stalinist period, Rajter was deemed "politically non-reliable"[citation needed] by the communist regime of the time, which led to a prohibition on his conducting.

In 1968 he returned as the chief conductor of the Czecho-Slovak Radio Symphony Orchestra, remaining there until his retirement in 1976.

In 1970 he conducted the nine symphonies by Ludwig van Beethoven for the first time in Bratislava as a complete cycle, a project for which he received the Ján Levoslav Bella Prize in the following year.

In 1991, Hungary appointed Ľudovit Rajter as an honorary member to the Savaria Symphony Orchestra in Szombathely for life.