Frances Bean and Isaiah Silva officially divorced back in November and Cobain's guitar has been at the centre of the two-year legal battle.
Lee appealed the ruling previous year, in which Courtney Love (Cobain's widow) and his daughter Frances Bean both filed documents and testified to block Lee's case.
The 1959 Martin D-18E acoustic guitar was famously played by the rocker during his iconic MTV Unplugged performance in 1993, shortly before his death.More news: Paddy Power to buy New York-based fantasy sports site
However, the daughter of Kurt and Courtney Love was keen to move on according to insiders, so gave up the fight, six months after their divorce was finalised.
Sources told TMZ that the visual artist eventually gave up fighting for the instrument, as "she wanted Isaiah out of her life for good, and didn't want the mess of a trial to bog her down".More news: Sacha Killeya-Jones lands at North Carolina State
Earlier this month, Frances opened up to the Daily Front Row about what her late father would think of her own music.
Isaiah Silva is reportedly allowed to keep the instrument in his divorce settlement with the Nirvana icon's daughter.
She said: "I don't have an answer for that because I don't want to speak on someone else's behalf".More news: What Pope Francis said about Gaza killings, violence in middle
Courtney Love and Frances Bean Cobain have won a court case that seals the photos of Kurt Cobain's death. On one particular occasion, Mr Lee even filmed himself chasing a limousine for several miles that he thought I was a passenger in.