He alleges he "lost millions" after Dre and Iovine "improperly took control" of Beats through a "sham" transaction.
After severing ties with Monster, Beats was purchased by Apple for $3 billion (£1.9 billion).
In legal papers filed in California, Lee alleges rap producer Dr Dre was barely involved in creating the headphones that carried his name.
But the range quickly became a highly desirable brand with celebrities and music fans, and Dre's endorsement was key to its success.
When the firm was sold to mobile phone manufacturer HTC in 2012, Dre and Iovine made $100m (£66m) each, Forbes estimated.
But Lee claims the deal forced him to cut his share in the company from 5% to 1.25%. He says he then had no other option but to sell his remaining stake for $5.5m (£3.6m) near the end of 2013.
His legal case describes the HTC deal as "fraudulent" and "a sham" intended to shift ownership of Beats to Dre and Iovine.
HTC later sold its shares back to the Beats.
Lee says if he'd still had his 1.25% stake, he would have received more than $30m (£19.8m) in the Apple deal.
His original 5% stake would have been worth around $150m (£99m).