The transverse momentum (({p}{T})) spectra of inclusively produced ({\Lambda }{c}^{+}) baryons are measured via the exclusive decay channel ({\Lambda }{c}^{+}\to p{K}^{-}{\pi }^{+}) using the CMS detector at the LHC. Spectra are measured as a function of transverse momentum in proton-proton ((pp)) and lead-lead (PbPb) collisions at a nucleon-nucleon center-of-mass energy of 5.02 TeV. The measurement is performed within the ({\Lambda }{c}^{+}) rapidity interval (|y|<1) in the ({p}{T}) range of 5–20(\phantom{\rule{0.2em}{0ex}}\text{GeV/}c) in (pp) and 10–20(\phantom{\rule{0.2em}{0ex}}\text{GeV/}c) in PbPb collisions. The observed yields of ({\Lambda }{c}^{+}) for ({p}{T}) of 10–20(\phantom{\rule{0.2em}{0ex}}\text{GeV/}c) suggest a suppression in central PbPb collisions compared to (pp) collisions scaled by the number of nucleon-nucleon (NN) interactions. The ({\Lambda }{c}^{+}/{D}^{0}) production ratio in (pp) collisions is compared to theoretical models. In PbPb collisions, this ratio is consistent with the result from (pp) collisions in their common ({p}_{T}) range.