Aims. We characterize the molecular environment of classical T Tauri stars in Lupus observed with the Spitzer Space Telescope in our search for gas-rich disks toward these sources. Methods. Submillimeter observations of 12 CO, 13 CO, and C 18 O in the $J=3$–2 and 2–1 lines were obtained with the James Clerk Maxwell Telescope toward a sample of 21 T Tauri stars with disks in the Lupus molecular clouds. Pointings at the sources and at selected off-positions are presented in order to disentangle material associated with disks from ambient cloud material. Results. One source, IM Lup (Sz 82), was found with the double-peaked 12 CO and 13 CO profiles characteristic of a large rotating gas disk. The inclination of the disk is found to be ~$20^\circ$, with an outer radius of 400–700 AU. For most other sources, including GQ Lup with its substellar companion, the single-dish 12 CO lines are dominated by extended cloud emission with a complex velocity structure. No evidence of molecular outflows is found. Due to dense circumstellar material, compact C 18 O emission was detected toward only two sources. Future searches for gas-rich disks in Lupus should either use interferometers or perform very deep single-dish integrations in dense gas tracers to separate the cloud and disk emission.