Removal of the central solenoid is essential to realize an economical spherical tokamak fusion reactor, but non-inductive plasma start-up is a challenge. On the TST-2 spherical tokamak, non-inductive plasma start-up using lower-hybrid (LH) waves has been investigated. Using the capacitively-coupled combline (CCC) antenna installed at the outboard midplane, fully non-inductive plasma current ramp-up up to a quarter of that of the typical Ohmic discharges has been achieved. Although it was desirable to keep the density low during the plasma current ramp-up to avoid the LH density limit, it was recognized that there was a maximum current density that could be carried by a given electron density. Since the density needed to increase as the plasma current was ramped-up, the achievable plasma current was limited by the maximum operational toroidal field of TST-2. The top-launch CCC antenna was installed to access higher density with up-shift of the parallel index of refraction. Numerical analysis of LH current drive with the outboard-launch and top-launch antennas was performed and the results were qualitatively consistent with the experimental observations.