What part of Lamar are you on? South Lamar has signs specifically addressing this-- BICYCLES MAY USE FULL LANE. It is there because staying on the road is way safer than trying to weave on and off between the sidewalk and bike lanes.

To give some context to other posters: It is legal to ride on the sidewalks in most of Austin, except for several streets downtown on the University of Texas campus. FRAP applies everywhere else. Bikes are only explicitly prohibited from several major freeways/controlled entrance roads. The only real MUP that can be used for transportation runs E/W along the river downtown.