Connecting fiber between a 1G SFP and a 10G SFP, will it work?

I've got a fiber handoff from an ISP that is using a 1G LX SFP module. This connects over SMF to my 10G LR SFP module on my core switch. However, they don't seem to like this situation, which begs the question: does this work? Or do both ends always need to be the same module type?