SR definitely won't work.  SR generates a multi-mode signal.  It expects a 50 micron core and has a different propagation pattern than single-mode.  LR generates a single-mode signal.  A single-mode fiber core is 9 micron.  It travels farther than a multi-mode signal.

This concept applies whether it's 1 Gb or 10 Gb.  Or higher.

it definitely won't work. 10GBASE-SR uses multimode fiber, while 10GBASE-LR operates over single-mode fiber. Maybe a mode conditioning patch cable will help you to solve this problem.