We have studied the superconducting properties of LaIr$_3$ with a rhombohedral structure using magnetization, heat capacity, and muon-spin rotation/relaxation ($mu$SR) measurements. The zero-field cooled and field cooled susceptibility measurements exhibit a superconducting transition below $T_{mathrm{C}}$ = 2.5 K. Magnetization measurements indicate bulk type-II superconductivity with upper critical field $mu_0H_{mathrm{c2}}(0)$ = 3.84 T. Two successive transitions are observed in heat capacity data, one at $T_{mathrm{C}}$ = 2.5 K and a second at 1.2 K below $T_{mathrm{C}}$ whose origin remain unclear. The heat capacity jump reveals $Delta C$/$gamma T_{mathrm{C}} sim$ 1.0 which is lower than 1.43 expected for BCS weak coupling limit. Transverse field-$mu$SR measurements reveal a fully gapped $s-$wave superconductivity with 2$Delta(0)/k_{mathrm{B}}T_{mathrm{C}}$ = 3.31, which is small compared to BCS value 3.56, suggesting weak coupling superconductivity. Moreover the study of the temperature dependence of the magnetic penetration depth estimated using the transverse field-$mu$SR measurements gives a zero temperature value of the magnetic penetration depth $lambda_{mathrm{L}}(0)$ = 386(3) nm, superconducting carrier density $n_{mathrm{s}}$ = 2.9(1) $times$10$^{27}$ carriers $m^{-3}$ and the carriers effective-mass enhancement $m^{*}$ = 1.53(1) $m_{mathrm{e}}$. Our zero-field-$mu$SR measurements do not reveal the spontaneous appearance of an internal magnetic field below the transition temperature, which indicates that time-reversal symmetry is preserved in the superconducting state of LaIr$_3$.
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