Lil the Dancer is a woman of bizarre appearance who performed bizarre actions as an FBI method, devised by Regional Bureau Chief Gordon Cole, to quickly and covertly brief Special Agent Chester Desmond on what to expect during his investigation into the death of Teresa Banks.
She wore a sour face, meaning that Desmond would have problems with the local authorities; they would not be receptive to the FBI.
Both of her eyes were blinking, which meant that there would be trouble higher up.
She had one hand in her pocket, meaning local authorities were hiding something.
Her other hand was made into a fist, indicating that the local authorities were likely to be belligerent and aggressive.
She is walking in place meaning that there would be a lot of legwork involved in the investigation.
Cole stated that Lil was his "mother's sister's girl." Missing in that sentence was the word "uncle"; this was then elaborated on when Cole placed four fingers in front of his eyes like prison bars. This suggested that the uncle of the sheriff was in prison.
Her dress had been tailored (with different-colored thread) to fit Lil, this being a code for drugs being involved with the investigation.
The meaning of the blue rose is never explained in the course of the movie and is left to the viewer's imagination. There is an article on the blue rose at Twin Peaks Studios, a website with explanations for many mysteries in Twin Peaks. The blue rose can be a reference to the Project Blue Book, UFOs' studies cited several times during the series.
By pure coincidence, Lil's actress, Kimberly Ann Cole, shares her surname with Gordon Cole.