A lumen is not brightness, a lumen is output. Let's go with output per area (Photons per area, so to speak, accounting for human sensitivity). Given that 1 lux is 1 lumen per square meter, use this table:
Source from Wiki
[TABLE="class: wikitable"]
[TR]
[/TR]
[TR]
[TD]120,000 lux[/TD]
[TD]Brightest sunlight[/TD]
[/TR]
[TR]
[TD]110,000 lux[/TD]
[TD]Bright sunlight[/TD]
[/TR]
[TR]
[TD]20,000 lux[/TD]
[TD]Shade illuminated by entire clear blue sky, midday[/TD]
[/TR]
[TR]
[TD]10,000 - 25,000 lux[/TD]
[TD]Typical overcast day, midday[/TD]
[/TR]
[TR]
[TD]<200 lux[/TD]
[TD]Extreme of darkest storm clouds, midday[/TD]
[/TR]
[TR]
[TD]400 lux[/TD]
[TD]
Sunrise or
sunset on a clear day (ambient illumination).[/TD]
[/TR]
[TR]
[TD]40 lux[/TD]
[TD]Fully overcast, sunset/sunrise[/TD]
[/TR]
[TR]
[TD]<1 lux[/TD]
[TD]Extreme of darkest storm clouds, sunset/rise[/TD]
[/TR]
[/TABLE]
For comparison, nighttime illuminance levels are:
[TABLE="class: wikitable"]
[TR]
[/TR]
[TR]
[TD]<1 lux[/TD]
[TD]
Moonlight[3][/TD]
[/TR]
[TR]
[TD]0.25 lux[/TD]
[TD]Full Moon on a clear night
[4][5][/TD]
[/TR]
[TR]
[TD]0.01 lux[/TD]
[TD]Quarter Moon[/TD]
[/TR]
[TR]
[TD]0.002 lux[/TD]
[TD]Starlight clear moonless night sky including airglow
[4][/TD]
[/TR]
[TR]
[TD]0.0002 lux[/TD]
[TD]Starlight clear moonless night sky excluding airglow
[4][/TD]
[/TR]
[TR]
[TD]0.00014 lux[/TD]
[TD]Venus at brightest
[4][/TD]
[/TR]
[TR]
[TD]0.0001 lux[/TD]
[TD]Starlight overcast moonless night sky
[4][/TD]
[/TR]
[/TABLE]
So if you have a 1 lumen light shining evenly on 1 square meter, then it's about like bright full-moon light. That same lumen spread over a 1cm square will look as bright as an overcast day.