That's not totally correct. With the zoom method you are not losing brightness, but with an anamorphic lens you are gaining brightness...
The lumen number gives you the luminous flux that the projector radiates. This is independent of a specific area.
The brightness you perceive on a specific area that is illuminated by the projector is called luminance and typically given in foot-lambert (fL).
Luminance = luminous flux / illuminated area.
With or without an anamorphic lens the projector always radiate the same luminous flux (lumens) (simplified because the A-lens absorbs and reflects some light)
But the illuminated area will be different.
Lets say your projector has 2000 lumen and your screen is 10' wide and the native panel AR is 16:9.
If the screen is 16:9 it would be 5.625' high, the (illuminated) area would be 56.25 ft² and the luminance then would be 2000/56.25 = 35.6 ftL (supposed the screen gain is 1.0)
If you have a cinemascope-screen with the same width of 10', height would be about 4.17', the area of the screen would be 41.7 ft².
When using the zoom-method, the illuminated area would be the same as with the 10' wide 16:9-screen! With the cinemascope-screen, the black bars are projected outside of the screen and with the zoom method they will still be there and contribute to the illuminated area, so the luminance will be the same as with the 10' wide 16:9 screen.
So you don't lose any lumens here.
With an anamorphic lens, the actually illuminated area will be changed! Now the illuminated area would be the same as the visible area of the cinemascope-screen, about 41.7 ft², the projector (roughly) radiates the same luminous flux of 2000 lumens, but the luminance now would be 2000/41.7 = 48 fL!
So you don't lose any lumens, and you don't lose luminance (brightness) with the zoom method, but you gain luminance with an anamorphic lens!
Theoretically about 33% but in reality the A-lens "swallows" some light as it absorbs it or reflects it back to the projector etc.
So the real gain of luminance with an A-lens wouldn't be that high. It depends on the quality of the lens (or prism) how much gain there will be.