All four thirds sensor cameras use built-in lens profiles. This message indicates LR is using the camera embedded lens profile information for correcting Distortion and Vignetting. You should NOT apply an additional lens profile using the drop-down selector.
Thanks for your answer. I've read this fact for the Micro Four Thirds Manufactureres but does this match also for the Sony APS C Lenses?
If you're seeing the below 'i Built-in Lens Profile applied' message in the Lens Profile tab then LR is using an embedded lens profile created by the camera. Click on the 'i' icon for more information. In the case of the below Canon camera it does not mention vignetting correction, but it is applied by the built-in profile. You should NOT apply an additional lens profile using the drop-down selector, which as you mentioned will double-correct the image.
If you're NOT seeing the 'i Built-in Lens Profile applied' message you should select and apply the appropriate lens profile from the drop-down selector. Normally the correct lens profile will be automatically detected and selected when you check 'Enable Profile Corrections.