Hi,
You can find transceivers specifications on this link:
https://support.hpe.com/hpsc/doc/public/display?docId=a00028947en_us
As a general rule, use the same transceiver specification on both ends of the link.
Your scenario is atypical: 10G-LR on one end and 10G-LRM on the other.
You will have to try and verify if the link works properly with the risk of damage the trasnceivers.
If I take the risk, I would use 9/125 um Single Mode Fiber (SMF) and a distance below 300m.
You would have to verify that the received power on each end is in the range of the supported power of the transceiver of that end, just to validate if it is enough power in order to detect the signal or just not to damage the transceiver.
See values on tables 23 and 24 on the link above.
Regards