Abstract In Montero-Dorta et al., we show that luminous red galaxies (LRGs) from the SDSS-III Baryon Oscillation Spectroscopic Survey (BOSS) at z ∼ 0.55 can be divided into two groups based on their star formation histories. So-called fast-growing LRGs assemble 80 per cent of their stellar mass at z ∼ 5, whereas slow-growing LRGs reach the same evolutionary state at z ∼ 1.5. We further demonstrate that these two subpopulations present significantly different clustering properties on scales of ∼1−30 Mpc. Here, we measure the mean halo mass of each subsample using the galaxy–galaxy lensing technique, in the ${\sim }190\deg ^2$ overlap of the LRG catalogue and the CS82 and CFHTLenS shear catalogues. We show that fast- and slow-growing LRGs have similar lensing profiles, which implies that they live in haloes of similar mass: $\log (M_{\rm halo}^{\rm fast}/h^{-1}\mathrm{M}_{{\odot }}) = 12.85^{+0.16}_{-0.26}$ and $\log (M_{\rm halo}^{\rm slow}/h^{-1}\mathrm{M}_{{\odot }}) =12.92^{+0.16}_{-0.22}$. This result, combined with the clustering difference, suggests the existence of galaxy assembly bias, although the effect is too subtle to be definitively proven, given the errors on our current weak-lensing measurement. We show that this can soon be achieved with upcoming surveys like DES.