We study theoretically the emission and lasing properties of a single nanoshell spaser nanoparticle with an active core and a plasmonic metal shell. Using time-dependent equations for the gain medium and metal, we calculate the lasing threshold through an instability analysis. Below threshold, the nanoshell acts as an optical amplifier when excited by an external probe field, while above threshold, it enters a regime of autonomous lasing. At the gain threshold, the lasing starts at one frequency, typically a plasmon resonance of the nanoparticle. With increasing gain, the emission then broadens to additional frequencies. This result contrasts with previous findings reporting only a single emission wavelength above threshold. We also compute the full spectrum and linewidth of the nanolaser, revealing strong frequency shifts and an asymmetrical lineshape. Finally, we demonstrate that the emission line can be tuned across the visible spectrum by modifying the aspect ratio of the nanoshell.