Inspired by anarchist pedagogies,[6] the school grew out of the LungA Art Festival, and was founded by Danish artist Jonatan Spejlborg Juelsbo and Icelandic artist and musician Björt Sigfinnsdóttir, the festival's co-founder and director.

[7][8] Like the festival before it, the school's name is a portmanteau of the Icelandic words 'lista' (art), 'ungur' (young) and 'Austurlandi' (East).

[15] Programs at the school were originally named '84' after the number of days of their duration.

[18] Many of LungA School's buildings and facilities are co-opted from local industry, either occupying spaces underused outside of Seyðisfjörður's busy tourist season or redeveloping spaces vacated by changes to the local fishing industry.

[21][22] American British artist and curator Mark Rohtmaa-Jackson was hired as the new director of the school in October 2023,[23] although the school aims for collaborative and decentralised organisational practices.