For LTO, older tapes are backward compatible with newer drives as follows:
- The previous generation tape can be read/written.
- The generation previous to that can be read.
- Generations before that are not compatible.
So, for example, an LTO-4 drive can read/write LTO-4, can read/write LTO-3, can read LTO-2, and is incompatible with LTO-1.
Newer tapes cannot be used in older drives under any circumstances. So, to the OP, an LTO-3 tape cannot be used in an LTO-2 drive.