Lightroom does not preserve the GR's JPEG profiles with DNG files. While it does support that behavior with a few manufacturers, I think it's a combination of enhanced functionality of that manufacturer's proprietary RAW format and/or Adobde considering them more high-volume manufacturers (think Canon/Nikon/whatever). So, no dice with Ricoh DNGs.
I don't typically like to work with JPEGs in Lightroom or similar programs most of the time. I'd say the GR files are significantly better than micro four thirds JPEGs if you do want to do some post work to them, but not nearly as good as the files form my Pentax K1 II. However, the good news is that the JPEG engine in-camera is really, really good and the RAW conversion options are extensive. My normal course of action is to take RAW or RAW+JPEG, then edit the RAW till I get a look I really want and save this as an extra JPEG (you can save as many as you want). Unless you need to seriously change the levels (which is the one area where I feel the camera engine struggles), you can get things pretty much taken care of in-camera.
If you're desperate for positive film, Samuel Streetlife sells a set of Lightroom/Photoshop presets which come quite close, they cost me $10 if I remember right so definitely not unreasonable.