AbstractTo extend the molecular gas measurements to typical L* star-forming galaxies (SFGs) at z ∼ 1.5 − 3, we have observed CO emission for five strongly-lensed galaxies selected from the Herschel Lensing Survey. The combined sample of our L* SFGs with CO-detected SFGs at z >1 from the literature shows a large spread in star formation efficiency (SFE). We find that this spread in SFE is due to variations of several physical parameters, primarily the specific star formation rate, but also stellar mass and redshift. An increase of the molecular gas fraction (f_gas) is observed from z ∼ 0.2 to z ∼ 1.2, followed by a quasi non-evolution toward higher redshifts, as found in earlier studies. We provide the first measure of f_gas of z >1 SFGs at the low-stellar mass end between 10^9.4 < M∗/M_⊙ < 10^9.9, which shows a clear f_gas upturn.