From this paper about the LORRI camera:
LORRI is a narrow angle (field of view=0.29°), high resolution (4.95
μrad pixels), Ritchey-Chrétien telescope with a 20.8 cm diameter
primary mirror, a focal length of 263 cm, and a three lens
field-flattening assembly. A 1024 × 1024 pixel (optically active region), thinned,
backside-illuminated charge-coupled device detector is used in the
focal plane unit and is operated in frame transfer mode.
If we take the field of view, 0.29 degrees or 5.061 mrad (milliradian) and calculate the angular resolution of the telescope for a medium wavelength of 600 nm and a diameter of 0.208 m, we get 2.91 µrad using the formula
$R = λ/D$
$R$ is the angular resolution, $λ$ the used wavelength and $D$ the diameter of the telescope.
See wikipedia for the formula of the angular resolution of a telescope.
When we divide the field of view (5.061 mrad) by the calculated angular resolution (2.91 µrad), we get the maximum number of pixels 1737. Using a 1024 × 1024 pixel sensor is therefore a good choice.
A 2048 * 2048 pixel sensor could deliver more pixel data, but not more image information. The maximum angular resolution of the telescope is defined by the diameter of the telescope and the used wavelength. To get a better resolution, we need a telescope with a larger diameter.