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We present the Differentiable Lensing Lightcone (DLL), a fully differentiablephysical model designed for being used as a forward model in Bayesian inferencealgorithms requiring access to derivatives of lensing observables with respectto cosmological parameters. We extend the public FlowPM N-body code, aparticle-mesh N-body solver, simulating lensing lightcones and implementing theBorn approximation in the Tensorflow framework. Furthermore, DLL is aimed atachieving high accuracy with low computational costs. As such, it integrates anovel Hybrid Physical-Neural parameterisation able to compensate for thesmall-scale approximations resulting from particle-mesh schemes forcosmological N-body simulations. We validate our simulations in an LSST settingagainst high-resolution $\kappa$TNG simulations by comparing both the lensingangular power spectrum and multiscale peak counts. We demonstrate an ability torecover lensing $C_\ell$ up to a 10% accuracy at $\ell=1000$ for sources atredshift 1, with as few as $\sim 0.6$ particles per Mpc/h. As a first use case,we use this tool to investigate the relative constraining power of the angularpower spectrum and peak counts statistic in an LSST setting. Such comparisonsare typically very costly as they require a large number of simulations, and donot scale well with the increasing number of cosmological parameters. Asopposed to forecasts based on finite differences, these statistics can beanalytically differentiated with respect to cosmology, or any systematicsincluded in the simulations at the same computational cost of the forwardsimulation. We find that the peak counts outperform the power spectrum on thecold dark matter parameter $\Omega_c$, on the amplitude of density fluctuations$\sigma_8$, and on the amplitude of the intrinsic alignment signal $A_{IA}$.

Forecasting the power of Higher Order Weak Lensing Statistics with automatically differentiable simulations