Yes, so long as the oil used has the API classification for Diesel engines AND gasoline engines, you will have no problems.
Oil classified for gasoline engines is alright to use in propane and natural gas fueled engines.
API classification for Diesel engines will begin with the letter "C" followed by some other characters. The current API class for Diesel lube oil is CJ-4.
API classification for gasoline engines will begin with the letter "S".
The current API classification for gasoline engines is SN.
If the oil in question has BOTH Cx AND Sx classification declarations, it can be used in engines of all fuel types.
Is this a compromise? I don't know. We now have some Toyota 4Y engines in our fleet that run on propane that currently have more than 40,000 hours on the meter. Engines are still running strong, have good compression, are not oil burners, and pass emissions test.