The mystery of 'Lyle' has remained (as I think he knew it would), sadly, now for 12 years and it is still poignantly haunting the minds of even more people.
I believe that the scrunched-up hand written note that read, 'SUICIDE' was written by Lyle and left in his room in a very obvious place when he was observed alternately, 'pacing' and 'walking' beside the two-lane highway, as described by the hotel manager.
I think he was contemplating throwing himself out in front of a passing car but decided that this might be an unsuccessful method of suicidal operation, in that it might be that he might cause an accident of some type if a car swerved to avoid him, or that he might actually be injured and left alive but maimed and so he chose to abort this idea.
Upon returning to his room he then screwed up the note and threw it in the waste bin as it would not be required to prove that hanging himself was an intentional act.
I think he fully recognised that throwing the screwed up message 'SUICIDE' into the waste basket was a symbolic representation of the action he was about to engage in that was the throwing away of his life by committing suicide.
I believe after reading the (very much appreciated) actual investigating officer's special contributions to this forum that Lyle was a medically educated and trained person because of the comments made on the nature of his studious handwriting, and the fact that he chose to choke off both of his carotid arteries with a ligature and even knew that there would be some jerking spasms after he lost consciousness which might rouse neighbors in the next room, hence the placement of the pillow against the wall in the closet. That kind of knowledge isn't general in society.
However, it's also possible that if there was, as speculated, a backpack accompanying 'Lyle' when he arrived at the motel then it contained something which he had arranged to give to someone he was to rendezvous with at the side of the highway on the same day the manager saw him pacing beside the highway.
That may well have been money and could have been in connection with the recent events of the attacks on the U.S. of September 11, 2001.
I doubt that idea though.