Lightroom does not use the Camera Raw plugin. That's for Photoshop.
Update your Photoshop CC to use Camera Raw 9.8. Help > Updates.
When I press Help > updates it just takes me to the CC app. The camera raw CC says its up to date.
In Photoshop, click Photoshop (Mac) or Help (Win) > About Plug-Ins > Camera Raw
Which version is shown?
showing version 126.96.36.1991
Do you have the Adobe Creative Cloud Desktop app installed. If you don't install it and check for updates in that. If you do open it and check for updates.
PS should be version CC 2017. What exact version are you running?
I have lightroom 6 and PS CS6, and get the same message. At the Camera Raw Download page, it is clearly written, that for CS6 I should use Camera Raw 9.1.1. So I installed this version, and get the same message again from Lightroom, saying I´d need camera raw 9.8 instead...
Seems very contradicting to me, no?
Thanks in advance for your appreciated help
No. You are using a newer version of LR that has an updated version of ACR built in and an older version of PS that has an older version of ACR plugin.
Always in that case you will get a warning dialog asking to send a Copy of the RAW file with LR edits applied and that Copy will be converted to either a TIFF or PSD file before it is sent to your older version of PS. The TIFF or PSD option is something you set in the LR Preferences on the External Editing tab.