I would have a whole lot to say about this and so I might have to get back to this with a more detailed answer that actually answers some of your questions, but in the meantime you might want to look into photosynthetically active radiation(PAR), because lumens won’t really be the best way to determine what you are trying to determine.
Watts would be the more accurate number overall than lumens because the goal of any light is to try and turn 100% of the electrical watts into 100% PAR watts, or 100% of the type of light watts that a plant can use, which would mostly be in the blue and red spectra, but this almost never happens as a lot of the electrical watts is lost in heat energy(infrared light/radiation) and or other less useful energy such as green light. Watts is a measurement of energy, and energy can exist as matter or any of the forms of the electromagnetic spectrum, i.e. electricity, visible light, as well as all the rest of the radiated spectrum – heat/infrared light/radiation, uv radiation, gamma rays, x-rays, etc. It can get quite complicated.
And really most people use yield per area more than yield per watt anyway since most people are going to try and put as much light per the area as they can anyway. Everyone will be trying to get around 30 - 50 watt per square foot no matter the type of light as this is the industry standard. And this is all an attempt to replicate the sun anyway, and so for example if you have the lights set up correctly for your area you should get similar yield per square foot as you would per square foot outdoors. Making yield per area the best way to anticipate yield for a given growing area, indoors or out.
The proverbial “gram per watt” is a goal more than a way to estimate or anticipate yield.