 If you liked
Kanojo wa Uso wo Aishisugiteru
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 ...then you might like
Aishiteru tte Ittemo Ii yo
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The music industry, songwriters and romance - these are shoujo/ josei manga that where the female mc is approached by a songwriter who keeps his identity hidden and needs a female muse / gf in order to create his best songs. The guys both have previous hits and need the inspiration of a new muse to bring out the romance in their music, they also don't mind using the girl for their own purposes. In Kanojo, the female lead is also a singer, but in Aishiterutte, she is not.