The RCTIP (Recommended Cold Tire Inflation Pressure for street use) for the 275/60R20 SL 115T tires on your LX570 is
30psi F/R.
The RCTIP for the LT285/55R20 Load Range E 122/119T tires on your LX570 is
43psi F/R.
I stand behind those two recommendations. The following, however, is just my opinion:
The 275/60R20 tires are a Standard Load 4-Ply rated tire. Personally, I would not choose this tire for aired-down use offroad. If, however, you do eventually choose this tire, and you have at least one (preferably two) spare(s) of the same size, and you must use it offroad, and must air down... I would not go below 22-25psi and I would take it easy - those sidewalls are paper thin.
The LT285/55R20 tires on the other hand, are a Load Range E 10-Ply rated tire - very suitable for aired-down offroad use. I agree with
@TimCFJ40 above and would recommend a starting point for a reduced pressure of half the street pressure, or in this case, 22psi. Also as
@TimCFJ40 stated above, for prolonged offroad speeds above 20mph or so, I would go a few psi higher.
HTH