Is it normal for RAW files to have lens distortion? How best to deal with it?

Is this normal for RAW images?

Yes, it is normal.

Based on my experience with Canon cameras with different lenses, the RAW image remains uncorrected w.r.t. to the corresponding JPEG.
This means that the following corrections are not applied (and can be applied separately in a RAW conversion program):

  • Colour corrections with picture profiles.
  • White balance corrections.
  • Noise “corrections”, i.e. denoising.
  • Lens corrections

How to best deal with the lack of correction in RAW images?

Use the Lightroom Lens Corrections panel.

You don’t need to eyeball it if you used a lens that is supported by Lightroom’s lens correction module.

Assuming the lens is supported, you can select all photos taken with that lens and apply the appropriate lens correction profile:

  1. In the Lens Corrections panel of the Develop module, click Profile and select Enable Profile Corrections.
  2. To change the profile, select a different Make, Model, or Profile.

There are additional steps to the process for more advanced tweaking, you can view them on the linked Lightroom help page.

Is the required correction the same for all RAW images of a camera + lens combo?

No, they required correction also depends on the used focal length, the aperture, focus distance and your personal taste.

Lightroom uses the correction profile to derive from the lens settings (aperture, focal length) what kind of correction it needs to apply. The correction is therefore not exactly the same for every RAW image, but is exactly the same for the same lens, aperture and focal length.

Of course, you have the (artistic) freedom to apply another amount of lens correction than LR suggest, depending on the scene or the look you’re going for. However, I find the default setting great to apply on all the photos (per lens) as a starting point and then tweak it from there.