There have been calls for the bikeway to be renamed -- but Austin's mayor Lee Leffingwell says he has no plans to amend this homage to Armstrong.
So as they whizz past Armstrong's name emblazoned on square, green and white signs, Austin's cyclists have a permanent reminder of his deeds -- good and bad.
"Lance is a very divisive topic," Martinez explained. "There are people who really believe he was persecuted and it's not fair what's happening to him.
"Then there are others who feel he is getting exactly what he deserves, there's a reputation of Lance as a bit of a jerk and this [the doping] was part of his win-at-all-costs personality.
"There is a sizeable part of the community who really don't care one way or another.
"We as people want to believe he overcame cancer and he won the most grueling bicycle race in the world, and he did it seven times in a row.
"But cycling was here before Lance got here and it'll still be here long after we've forgotten him."
Back at the 15-year-old Livestrong Foundation charity, which has raised more than $500 million to support cancer patients, donations have increased since the allegations linking Armstrong with serial doping.
"It might be that people are learning about the work of the foundation as a result of the controversy from the cycling world," mused Livestrong spokeswoman Katherine McLane. "In which case that is a positive effect."
Armstrong stood down as chairman of the Livestrong Foundation in October, the same month the organization also legally changed its name from the Lance Armstrong Foundation.
McLane says it's his work with the foundation that should remain as Armstrong's lasting legacy -- not the implosion of his cycling career.
"I would say that Lance's greatest legacy is creating an organization that has helped 2.5 million people when they are facing cancer," she added.
"He's still the foundation's biggest donor. He's donated $7m."
Amid all the opinion and rhetoric bubbling around Armstrong in Austin, there was no sign of the man himself.
His only public appearance since the scandal enveloped him was at a Livestrong gala on October 20 and when Formula 1 made its debut in the city, Armstrong flew to Hawaii to avoid the hubbub.
Suzanne Halliburton, who has followed Armstrong's rise and fall for the Austin Statesman newspaper since 1996, is one of the few still in regular contact with Armstrong.
"The last time I talked to him he seemed to be doing reasonably well," she told CNN. "He has access to a private plane where he can zip off and go hang out in Hawaii at his house there."
Armstrong, who also has a Spanish-style villa close to downtown Austin, has no reason to keep out of the public gaze in his hometown, according to Halliburton.
"When he rides he goes out to Hill Country but his house is in central Austin," she explained.
"He's got five kids, two of whom live with him. He's very active, going to see all their sporting events, sometimes coaching their soccer teams. He sits in line to pick up the kids.