The easiest way to come to the lab is to take the subway. Line B, direction Ramonville, Stop "Saouzelong". Then walk to the lab (see below)
From the train station "Gare Matabiau SNCF": Take the subway, line A, direction "Basso-Cambo", change to line B at the first stop "Jean-Jaurès". Take line B, direction "Ramonville", stop "Saouzelong"
From the airport "Toulouse-Blagnac": 2 options:
Cheap and slow: Take the tramway line T2 at the airport to "Palais de Justice". At "Palais de Justice", take the subway, line B towards "Ramonville" and stop at "Saouzelong" €1.6. More than 45 minutes
Faster and more expensive: take the shuttle to downtown. Get down at the first stop "Compans -Cafarelli", take the subway, line B towards "Ramonville" and stop at "Saouzelong" - €8 one way. About 35 minutes
You can also take a cab. This is generally the fastest option (about 20 minutes), except at peak hours (8-9 in the morning, 17-19h i the afternoon). About €35
Finally, a nice option is "Velo Toulouse". €1/ bike rent. 30 min free. More info here (sorry, I did not find an English version)