Lance Armstrong's GF -- The Couple that Surfs Together ... Is Still Banned from Most Other Sports

Despite the fact he lied ... cheated ... falsely accused others ... and embarrassed his country ... there's still one person who's got Lance Armstrong's back -- his girlfriend Anna Hansen.

Lance and Anna (who have been dating since 2008) were stand-up paddle boarding together in Hawaii the other day.

It's one of the only activities Lance is allowed to participate in ... since he was banned from cycling, triathlons and just about every sport that requires its players to not be a lying, doped up cheater.