A little enhancement to the eyes of your subject adds a little extra pop and elevates the whole image.
Whether using Lightroom adjustment brushes or Photoshop, the basic principle is to add contrast, brighten the iris and perhaps add some spectral highlights. Professional retouchers have a detailed process for this, but simple edits have good effects.
This image was taken with a flash so there is the added problem of the cat equivalent of red – eye.
I will be using Photoshop to make the enhancements. It is possible to make these changes in Lightroom, but the adjustment brush is a bit awkward for me so I prefer the fine control possible in Photoshop.
Replace the Red Eye caused by flash
Open the image and make a selection of the the pupil. You can start with a circle selection, but it may not be perfectly round so add to the selection if necessary.
Fill or paint black into the selection.
The black looks a bit flat so mix in a bit of dark gray to help give a shiney, reflective look.
Eyes usually have a white spot reflection in them called a spectral highlight which gives a lifelike effect. Add a dot of white off center in the pupil. Place the highlights in the other eye as if it is made by the same light source or the eyes will look a bit crazed.
Now we can add some pop. For those not concerned with non-distructive techniques (because you have the original raw file or another copy), you can use the Dodge and Burn tools. If you are less confident and want to make the changes on a separate layer(s) that it can be adjusted, use a layer and a paintbrush.
This image shows areas to dodge (lighten) start very lightly and build up the contrast .
The next step is just a tiny bit of color. The eyes are such a match to the color of the fur, a slight shift in hue will help them stand out. I added a bit of green to the eyes to set them apart from the color of the fur.
Other species have different shaped eyes, but the same principles can be used to enhance their eyes. Because careful not to overdue this technique because it can look fake and odd if too heavy handed: better to understate the enhancement than to overstate.