The lumen is the SI unit of luminous flux. It is the luminous flux per steradian (unit solid angle) of a source of luminous intensity 1 candela (also an SI unit)
Lux is the unit of illuminance, the luminous flux arriving at a surface, it has the unit lumens per square metre.
Pmol/m2s no idea Not a lighting unit as far as I know.
The distribution of light from LEDs is normally measured on a goniophotometer angle by angle and expressed as the luminous intensity in each direction in candelas. This can then be integrated and expressed as the total amount of light emitted in lumens.
The total amount of light may also be measured as a single value in an integrating sphere by comparison with a known source.