I 'm not an attorney, but I did spend twenty years in the entertainment industry as a lighting director working with bands, artists, and their management. Alas, you pose a question that has limited solutions for sure, as Chugan and artchain point out. However, I may have a twist on the issue that's worth consideration.
Chugan brings up a couple of points that warrant clarification before I continue. As for not being more concerned about perfecting your craft, there are hundreds of thousands of songwriters, novelists, etc. out there whose craft is well advanced, but they don't see the publishing light of day. The idea that someone's craft is deficient because they are “unknown” is a risky assumption, and your craft may already be up to speed.
As for learning the business and the answers becoming self-evident, I agree; however, there may be a shorter route to the lead singer. If your stuff is good---I mean, really good. If your lyrics for this band really rock, or whatever applies here, and you get them through the door, the band may very well pick up the project, especially if they are looking.
Artchain makes a good case for networking to find a legitimate agent. Yeah, and that's a tough route worth pursuing, but is it really the answer to your question?
This is my answer, and keep in mind: I'm a lighting-director-turned-writer, not an attorney.
If you don't have a “paper” yellow-pages in your house, go to a branch of your local library---they'll have it. Look up “entertainment/music” attorneys---something like that, and find the ones that will give you a free ten-minute or whatever consultation.
Contact all of them. However, before you call any of these people to ask if they do free consultations, put your question in writing so that it reads exactly the way you want it to read. Keep it under 30 seconds---a 30-second sound bite. Keep it simple and succinct---something like this.
“I'm an unknown lyricist. I've written the lyrics for an album project for a well-known, successful band, which I believe will interest them. I want the band to write the music for the lyrics. Since I'm an unknown entity with no track record, I'll obviously need someone to pitch the project on my behalf. I'd like to know who/what that person should be, and the mechanics of how best to pitch this project to the band.”
When you make these calls, you may actually get the attorney on the phone, and she may very well ask you what's on your mind right on the spot. So, have the question/statement on hand, and if that happens, read it just like you have it written. Don't ad lib and stumble around with ah, well, uh, like, okay here's, etc.---just read it, word for word.
If you have to set up the consultation, set it up, and go, and read the pitch word for word. If the attorney asks, tell them you'd like the industry standard music/lyrics financial arrangement. They'll know exactly what that is.
I'm thinking that an entertainment attorney who can gain access to the band---an attorney who represents other such artists they may know about, and is willing to pitch the work for you---will be your best bet.
Of course, this person may have to believe that you have your notes and bars in a row before they will put their reputation on the line by representing you, another reason why your work truly has to be up to speed.
Speaking of which, make sure you have your lyrics ready to present to an attorney and take them with you for each consultation---it's a crazy business, and you never know.
You may even have to pay for a consultation, but I don't think so.
Short of this, attend “songwriter” functions in your area if there are any, and ask the same question of working songwriters and other people in the business---networking, as Chugan and artchain suggest. However, I'm not talkin' about songwriter functions of “wannabe” songwriters---dreamers in writers groups.
BMI and ASCAP may have any number of contacts---songwriters and others---who could answer the question. Get on the Web and check out other Songwriting organizations.
Regardless, I still think an entertainment attorney may be the key to the door you need to open.