Back in the 1920's the lumen was a standard pentane lamp. I have often wondered
whether we ought to make them again.
You can calculate the power per unit area coming off a tungsten lamp filament,
but I doubt if this is helpful to you because you probably cannot measure the
geometry of the filament. To do this accurately, you will probably want
something exotic like a bath of freezing platinum. However, you do know the
total power going into the lamp, which has got to be equal to the total power
coming out. A lot of that will be in the infra-red, but you should be able to
estimate the visible fraction.
I suspect your lamp is not uniform. You could use an integrating sphere but
those waste so much light that you would no longer be sure of your absolute
power. Frosting the outside of the lamp, and using diffusers may help. I have a
standard lamp and an integrating sphere, so I am not making this up.
If you want to do stuff from first principles, then you can make a standard
detector. Look up bolometers, particularly Langley's bolometer. These detect
integrated radiation, so its reading will probably be dominated by the
infra-red. Langley's bolometer was able in 1810 to detect thermal radiation
from a cow a quarter of a mile away. Unfortunately, your spectrum will probably
be dominated by the heat coming from the lamp envelope.
I calibrate spectrometers using a helium lamp for wavelength, and a
PhotoResearch PR-701 for brightness with a diffuse incandescent source (an old
OHP filtered for approximate D65 balance) as a transfer standard.