If you convert your RAW files to DNG, then Lightroom will update the previews in them and Photo Mechanic will show them.
If you want your edits reflected, DNG is indeed the way to go. Since ditching Nikon Capture NX2 as my primary raw converter, I made the switch to DNG and have not looked back since! The only “problem” with Lightroom is, it doesn't automatically save the updated preview in the DNG, you have to tell it to do so explicitly. This is one of the many reasons I actually prefer Photoshops camera raw over Lightroom; ACR
does update the preview automatically.