A vocal coach could help Lil with her intonation and getting the different registers of her voice to work more smoothly, but her style is just not distinct enough. There are so many OTHER R&B artists out there who sound enough like her, but do it so much better.
Interestingly enough, David Cook had a serious theatrical background, but, personally, I had no interest in him and think he will prove to be a flash in the pan.
I also have an extended opinion on how many of the prior singers have been mis-packaged on their solo album(s). But, that's a real soapbox for me. LOL.
Producers create the identity of the artist on records and Adam should be easily produced because he has the vocal athleticism to do whatever is asked of him. If there is any real concern about him being "too theatrical", the producer would be able to work with that.
But, many of the greatest pop/rock vocal performers were extremely theatrical in their moves and delivery. Most of our vocalist, including one major artist who has come to sell millions and millions of records and has been a successful recording artist since the mid 1980s went for theatrical coaching when making his first demo recordings.
My vocal instructor had her BA in Music and her MA in Theater. They go hand in hand.