Can I update Lightroom with Camera Raw?

Quote. "Under Lightroom's about it says the version of Lightroom is 6.14 and Camera Raw plugin 10.1. Bit of a contradiction there."

Yes, that was unusual, LR 6.13 was ACR 9.13, so LR 6.14 would normally have been ACR 9.14, however, LR 6.14 was a bonus update and the last one for the licensed non-subscription and was updated with the latest version of ACR available at that time.

You need to check the version of ACR that your version of Photoshop has at the moment, it needs to be at least 10.1.

That might require a subscription version of Photoshop to run ACR 10.1.

Lightroom 6.1 is not Lightroom Classic. Lightroom 6 was the last standalone version of Lightroom. You have the first update, which was 6.1. The final update was 6.14 and it isn't readily available anymore. If you go to your account it might be available there. If not, you'll have to contact Adobe directly for a download to obtain it. Lightroom 6 is no longer updated nor supported by Adobe.

In any case, it is NOT possible to update Lightroom with the camera raw plug-in. Camera Raw is for Photoshop and Photoshop Elements. That technology is part of the Lightroom program, and the camera raw plug-in is simply used by the other program during the transition from Lightroom to either Photoshop or Photoshop Elements. The plug-in itself is not used in the Lightroom processing.

No, there's not a contradiction there. The message means that because Lightroom is at the 10.1 version of Camera Raw, when you choose to edit in Photoshop (which has its own Camera Raw plug-in), then Photoshop's Camera Raw plug-in should also be at version 10.1 or later, and that message indicates that it isn't.

If you are running Lightroom 6.14 (not the "last version of Lightroom Classic", which is currently at version 9.1), I assume you are using an older version of Photoshop. Open Photoshop and check its Camera Raw plug-in version, though I suspect it won't support Camera Raw 10.1.

In which case, you should choose the option to "Render using Lightroom" when you get that compatibility warning, which then uses Lightroom's Camera Raw engine to render the Tiff/PSD for opening into Photoshop (if the Camera Raw versions are fully compatible, Lightroom passes the raw file to Photoshop, which silently uses its own Camera Raw plug-in to create the Tiff/PSD). The only real difference to the user is that using Lightroom to render the file means the file is created on disk first....so if you subsequently decide to abandon the work in PS you'll be left with a stray Tiff/PSD file to delete. If PS renders the file, it's initially only created in the system cache, so only when you subsequently "Save" is the physical file created on disk. However, being an older version of Camera Raw it might not be able to correctly render some of the edit adjustments that you made in Lightroom using the newer version of Camera Raw, so using "Render using Lightroom" is usually the safer option for dealing with that compatibility issue.