Do the LCoG builds emphasize down travel while limiting up travel? In other words, is the shock 2/3+ of the way compressed at ride height?
If so, that would seem to be counterproductive to utilizing the shocks’ full travel.
It depends on who is doing the build and what their understanding of how the entire suspension system will work together. The LCOG term and philosophy has been bastardized a bit - it's basically the "overlanding" equivalent of a crawler. For a long time, the 1/3-up and 2/3-down travel split has been a very solid target for a "Jack of All Trades" build, with the notable exception of a high-speed, desert running rig.
There are a few issues with this - particularly in the constraints of the TJ - as others have pointed out. The biggest issue is the diminished amount of uptravel when compared to stock (which is generally accepted to be 4-4.5"), which causes chassis lift when going over obstacles. This causes tipping and general unstable balance through obstacles, rather than allowing your suspension to work for you.
The other big issue is lack of contact pressure. I was talking about this very topic not too long ago with someone who's very experienced and knowledgable on the topic (and who's been on Ultimate Adventure a few times and is a KOH regular). He said there is no hard answer but a good rule of thumb is that residual spring pressure should equal to tire weight. I haven't seen this mentioned in other resources but he noted that the entire build world is moving towards a more balanced travel setup and getting away from the RTI/flex shows.
**Edit for clarity**
By "residual spring pressure", it was described to me as follows - it is the amount of force the spring is able to apply downward due to the amount of compression on the spring. For example, if you have a 200#/in spring and your tire/wheel combination weights 100#, you want roughly 1/2" of compression at the end of suspension travel. If you have 175#/in springs and your tire/wheel combo weights 75#, you want roughly 7/16" of spring compression.