If Lambda software is made with machine code then it will often NOT work on both ROM versions because calls to ROM routines are very different.
The Lambda engineers almost refactored the entire ROM with version 2, so no code is in the same place. This meant software compatibility for machine code software with version 1 was broken.
You might not know this, but the Lambda ROMs can auto detect a ZX81 program on tape and convert it to Lambda format. It will often work if it’s pure Basic.
ZX81, Lambda 8300, Commodore 64, Mac G4 Cube