TOI-561 is a galactic thick disk star hosting an ultra-short period (0.45 day orbit) planet with a radius of 1.37 R\(_{\oplus}\), making it one of the most metal-poor (Fe/H = -0.41) and oldest (\(\sim\)10 Gyr) sites where an Earth-sized planet has been found. We present new simultaneous radial velocity measurements (RVs) from Gemini-N/MAROON-X and Keck/HIRES, which we combined with literature RVs to derive a mass of M\(_{b}\)=2.24 \(\pm\) 0.20 M\(_{\oplus}\). We also used two new Sectors of TESS photometry to improve the radius determination, finding R\(_{b}\)=\(1.37 \pm 0.04 R_\oplus\), and confirming that TOI-561 b is one of the lowest-density super-Earths measured to date (\(\rho_b\)= 4.8 \(\pm\) 0.5 g/cm\(^{3}\)). This density is consistent with an iron-poor rocky composition reflective of the host star's iron and rock-building element abundances; however, it is also consistent with a low-density planet with a volatile envelope. The equilibrium temperature of the planet (\(\sim\)2300 K) suggests that this envelope would likely be composed of high mean molecular weight species, such as water vapor, carbon dioxide, or silicate vapor, and is likely not primordial. We also demonstrate that the composition determination is sensitive to the choice of stellar parameters, and that further measurements are needed to determine if TOI-561 b is a bare rocky planet, a rocky planet with an optically thin atmosphere, or a rare example of a non-primordial envelope on a planet with a radius smaller than 1.5 R\(_{\oplus}\).