The Lithium Tokamak Experiment (LTX) is a spherical tokamak designed to study the low-recycling regime through the use of lithium-coated shells conformal to the last closed flux surface (LCFS). A lowered recycling rate is expected to flatten core $T_\mathrm{e}$ profiles, raise edge $T_\mathrm{e}$, strongly affect $n_\mathrm{e}$ profiles, and enhance confinement. To study these unique plasmas, a Thomson scattering diagnostic uses a $\le 20$~J, 30~ns FWHM pulsed ruby laser to measure $T_\mathrm{e}$ and $n_\mathrm{e}$ at 11 radial points on the horizontal midplane, spaced from the magnetic axis to the outer edge at a single temporal point for each discharge. Scattered light is imaged through a spectrometer onto an intensified CCD. The diagnostic is absolutely calibrated using a precision light source and Raman scattering. Measurements of $n_\mathrm{e}$ are compared with line integrated density measurements from a microwave interferometer. Adequate signal to noise is obtained with $n_\mathrm{e} \ge 2 \times 10^{18}\,\mathrm{m^{-3}}$. Thomson profiles of plasmas following evaporation of lithium onto room-temperature plasma-facing components (PFCs) are used in conjunction with magnetic equilibria as input for TRANSP modeling runs. Neoclassical calculations are used to determine $T_\mathrm{i}$ profiles, which have levels that agree with passive charge exchange recombination spectroscopy (CHERS) measurements. TRANSP results for confinement times and stored energies agree with diamagnetic loop measurements. Results of $\chi_\mathrm{e}$ result in values as low as 7 m$^2$/s near the core, which rise to around 100 m$^2$/s near the edge. These are the first measurements of $\chi_\mathrm{e}$ in LTX, or its predecessor, the Current Drive Experiment-Upgrade (CDX-U), with lithium PFCs.