Understanding optical parameters of image sensors
Lux is a photometric unit, energy units are radiometric units and the two are related through the response of the human eye.  The Lux will nominally have the same units as the radiometric units but it will be weighted by the "typical" eye response.  To make things easier to understand/compare when ever you see Lux think the radiometric terms in equivalence.

Sensitivity in \$\dfrac{V}{Lx \cdot S}\$: \$Lx\$ is a per unit area measure so the \$m^2\$ is implied.  Your TCD1201 must be wrong, the units should be \$\dfrac{V}{W \cdot s/m^2}\$ to be equivalent.

That now explains your confusion in that \$W \cdot s\$ is Joules.  So a reception of a given amount pf photon energy integrated over time will be a measure of Energy which corresponds to a Voltage signal.

Conversion efficiency:  Is the conversion of photons to electrons. From energy of light and wavelength you can derive the photon flux and energy per photon.  With Quantum efficiency and the transfer efficiency (moving the charge to the output node) these two terms combined give your your conversion efficiency, you get the number of charge carriers generated per photon.

Dynamic range: Has everything to do with the optical properties of the sensor.  Dynamic range ideally is limited by the shot noise of the sensor which tracks as the \${N}^\frac{1}{2}\$ with N being the number of photons.

SNR is also important as is it the ratio of SEE to NEE - Saturation equivalent exposure to noise equivalent exposure.