Everytime this has happened to me, it was one part of the secondary air system or another. Especially if it goes into 35 mph limp mode.
I have had this happen to me 4 times. Twice on a Tundra and twice on the LX470 that I have now. One of the times the vehicle never entered limp mode.
This...
Assuming I understand correctly - the Land Shark - shark net grills require and good bit of fitment and are far from bolt on. Not a deal breaker, but just worth noting it would want something with minimal changes to the factory mounting.
This may be another option for those looking.
Looks identical - no idea if it actually fits or not. Anyone ever ordered from these guys before?
https://teqcustoms.com/collections/lx470-grilles/products/trd-pro-grille-98-07-lexus-lx470-teq-customs
While I agree that it is good to fix the radiator shroud - I do not think this is your issue, especially since it has been like that for a while. If you have a working fan, and enough water flow I don't think you would have an issue in the state you have it.
I have run cars, granted, not LCs...