Prospects for searches for long-lived particles after the LHCb detector upgrades

The LHCb detector is a single-arm forward spectrometer covering the pseudorapidity range $2 < \eta < 5$, initially designed for the study of particles containing $b$ or $c$ quarks. As such, it is naturally suited for the search of beyond SM long-lived particles in a range of mass and lifetime not too dissimilar to heavy-flavour hadrons, as it has been demonstrated in several publications. Prospects for these searches in regard of future LHC upgrades, where challenging conditions are foreseen, are presented in this conference note with the goal to serve as an input for the HL-LHC and HE-LHC Yellow Report.