We present IRAM Plateau de Bure Interferometer 3mm observations of CO(1-0) emission in two 24um-selected starburst galaxies in the outskirts (2-3xR_virial) of the rich cluster Cl0024+16 (z=0.395). The galaxies inferred far-infrared luminosities place them in the luminous infrared galaxy class (LIRGs, L_FIR>10^11 L_Sun), with star formation rates of ~60 M_Sun/yr. Strong CO(1-0) emission is detected in both galaxies, and we use the CO line luminosity to estimate the mass of cold molecular gas, M(H_2). Assuming M(H_2)/L_CO = 0.8 M_Sun/(K km^-1 pc^2), we estimate M(H_2) = (5.4-9.1)x10^9 M_Sun for the two galaxies. We estimate the galaxies dynamical masses from their CO line-widths, M_dyn~1-3x10^10 M_Sun, implying large cold gas fractions in the galaxies central regions. At their current rates they will complete the assembly of M_Stars~10^10 M_Sun and double their stellar mass within as little as ~150Myr. If these galaxies are destined to evolve into S0s, then the short time-scale for stellar mass assembly implies that their major episode of bulge growth occurs while they are still in the cluster outskirts, long before they reach the core regions. Subsequent fading of the disc component relative to the stellar bulge after the gas reservoirs have been exhausted could complete the transformation of spiral-to-S0.
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