Ok, we are remodeling our lower level (still)

and my photo equipment stash is who knows where behind a pile of boxes. But I had some time last night and this AM and used my lux meter. I could also measure in foot candles but used the lux scale just because it gives higher numerical readings and therefore higher resolution. If you want to convert to nits or fl, there are charts for that.

Anyways, my lux meter seems to give lower readings than my photographic light meter. At least this will give you and idea of the rise in light output over time. This is just pretty quick and dirty as they say, but still should give a pretty fair representation of what you were looking for.
Max output after 105 minutes to 3 hours stabilized is 270 lux +/- 2 lux.
Output after specified time:
100 lux @ 3 min. 37%
193 lux @ 15 min 71%
235 lux @ 30 min 87%
251 lux @ 45 min 92%
261 lux @ 60 min 96%
267 lux @ 90 min 98.8%
270 lux @ 105 min 100%
The Back Light output was stable at 270 +/- 2 lux after 105 minutes and monitored for 4 hours total. So in my opinion, from now on, I wouldn't do any setting adjusts on my TV until it was on at least 60 minutes or better still 105 minutes. And, as you can see, it takes an additional 60 minutes to gain the last 8% in light output to max output. I will say that after 45 minutes to 1 hour I really can not tell visually, any "brighter" or better picture with either excellent OTA content or Blu-ray reference movie content.
Well, it's "summer" here already, mom's day and such and plenty of outdoor things to enjoy. Too nice to do much more indoor stuff like this unless it rains and then it's back at the lower level remod.

BTW. . . what are your figures for similar times? I know you said 2 hours to peak output I think.
P.S. A contact type photo sensor was used with the 1330B meter in the style of the D2 puck design. Reading with the TV off and low indirect ambient room light is 0.