Secondary halo properties beyond mass, such as the mass accretion rate (MAR), concentration, and the half mass scale, are essential in understanding the formation of large-scale structure and dark matter halos. In this paper, we study the impact of secondary halo properties on the galaxy-galaxy lensing observable, $DeltaSigma$. We build an emulator trained on N-body simulations to model $DeltaSigma$ and quantify the impact of different secondary parameters on the $DeltaSigma$ profile. We focus on the impact of MAR on $DeltaSigma$. We show that a 3$sigma$ detection of variations in MAR at fixed halo mass could be achieved with the Hyper Suprime Cam survey in combination with a proxy for MAR with scatter $sigma_{Gamma_mathrm{dyn}|mathrm{obs}}<1.5$. We show that the full radial profile of $DeltaSigma$ depends on secondary properties at fixed halo mass. Consequently, an emulator that can perform full shape fitting yields better than 2 times improvement upon the constraints on MAR than only using the outer part of the halo. Finally, we highlight that miscentering and MAR impact the radial profile of $DeltaSigma$ in a similar fashion, implying that miscentering and MAR need to be modeled jointly for unbiased estimates of both effects. We show that present-day lensing data sets have the statistical capability to place constraints on halo MAR. Our analysis opens up new possibilities for observationally measuring the assembly history of the dark matter halos that host galaxies and clusters.
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