A stacked-target of natural lanthanum foils (99.9119% $^{139}$La) was irradiated using a 60 MeV proton beam at the LBNL 88-Inch Cyclotron. $^{139}$La(p,x) cross sections are reported between 35-60 MeV for nine radionuclides. The primary motivation for this measurement was the need to quantify the production of $^{134}$Ce. As a positron-emitting analogue of the promising medical radionuclide $^{225}$Ac, $^{134}$Ce is desirable for in vivo applications of bio-distribution assays for this emerging radio-pharmaceutical. The results of this measurement were compared to the nuclear model codes TALYS, EMPIRE and ALICE (using default parameters), which showed significant deviation from the measured values.