The 'Gonna Make My Own Money' band's drummer, Julie Edwards, was fascinated by the troubled actress' short lived singing career - which saw her release one album, 'Speak', in 2004 - and would love for her to lend her voice to one of their tracks.
She told BANG Showbiz: ''Would we write a song for Lindsay? I think so, absolutely. I mean that's a really interesting topic to us, women's self esteem.
''It would be a like a steamy, swampy, slow blues number. The lyrics would be, 'Lindsay, Lindsay don't you do that to yourself girl'.
''She could do a little spoken piece over it. She has a really nice voice too, a deep textural voice.''
Julie added she was disappointed with Lindsay's singing career, because it didn't give much away about her real life.
She added: ''I was disappointed with the music. It was typical, it didn't sound like distinctively Lindsay to me, it sounded generic, dance pop party lifestyle culture.
''I really wanted it to reveal things about her. I wanted it to be her self-expression, but I felt it was more just an attempt to make money.''
Julie - who makes up Deap Vally with singer/guitarist Lindsey Troy - added she thinks most people have the wrong impression of 'The Parent Trap' star Lindsay, who is currently undergoing 90 days of court ordered treatment in a rehab facility in California.
She said: ''I think Lindsay, in all honesty, is probably incredibly strong, very bright, I bet she's probably an anarchic thinker. But I wouldn't call her a feminist role model because I think that she is too self destructive.''
Deap Vally's debut album, 'Sistrionix' is out now.
We want to speak to the Grammys manager...