In my living room, in ANY light condition, my OLED's better blacks are readily apparent compared to the outgoing Panasonic ST60 (measured at 0.002 ftl and after it was calibrated ANSI contrast of something like 15,000:1). Without doubt the darker the room the more the blacks standout, but the point is even with normal ambient lighting the better contrast of OLED is easily realized.
My reasonable guess is that a high end LCD's would fare about the same as the ST60, despite the extra brightness on tap. The best LCD's are getting something like 6,000:1 native contrast and boosted to around 15,000:1 with FALD, going on memory I think the best blacks they see is around 0.006 ftl, which isnt bad, but significantly higher than the ST60 that I compared with. The overall contrast ratio should be similar enough between a high end LCD and the ST60, so that is what I am making my assumption on. While LCD might get brighter than OLED's, the limited contrast ratio will be the limiting factor, and this is also noted by the phone screen examples above.
As a bad comparison to the LCD that I have, it does a bit over 300 nits full screen (almost double the OLED), is limited to about 1,400:1 contrast, and has a matte finish on the screen rather than a proper black filter. No matter the settings or light conditions it looks like a washed out mess. It is a far cry from a high end LCD, but an easy example of why contrast is more important than overall nits.