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In the realm of natural supersymmetric models, higgsinos are typically thelightest electroweakinos. In gauge-mediated supersymmetry breaking models, thelightest higgsino-dominated particles decay into a $Z$-boson or a Higgs boson($h$), along with an ultra-light gravitino ($\tilde{G}$) serving as thelightest supersymmetric particle (LSP). This scenario suggests a significantnon-resonant $hh$ production. Basing on the recent global fitting results ofthe $\tilde{G}$-EWMSSM (MSSM with light electroweakinos and an eV-scalegravitino as the LSP) performed by the \textsf{GAMBIT} collaboration, whichsupport a higgsino-dominated electroweakino as light as 140 GeV, we develop twosimplified models to evaluate their detection potential at the high-luminosityLHC (HL-LHC) with $\sqrt{s} = 14~{\rm TeV}$ and an integrated luminosity of$3000~{\rm fb}^{-1}$. The first model examines the processes where heavierhiggsino-dominated states decay into soft $W/Z$ bosons, while the secondfocuses on direct decays of all three higgsino-dominated electroweakinos into$W/Z/h$ plus a $\tilde{G}$. Our study, incorporating both models and theirdistinct decay channels, utilizes detailed Monte Carlo simulations for signalsand standard model backgrounds. We find that the HL-LHC can probe higgsinos upto above 500 GeV, potentially discovering or excluding the natural SUSYscenario in the context of a gravitino LSP. Further, we reinterpret thisdiscovery potential using the GAMBIT global fit samples, and find that theentire parameter space of $|\mu| \leq 500~{\rm GeV}$ with an electroweakfine-tuning measure ($\Delta_{\rm EW}$) under 100 in $\tilde{G}$-EWMSSM isaccessible at the HL-LHC.

HL-LHC sensitivity to higgsinos from natural SUSY with gravitino LSP