Yes, you can absolutely use Lightroom if you wish to use it instead of Capture One! That said, 95% of my students are very happy Capture One users after using it in my workshop, but each person needs to decide this for themselves.
Although the course is taught using Capture One (my recommendation), keep in mind that it is just used during the shooting sequence and that we are only using Capture One to adjust exposure and enable the color balance presets (all of which is explained very clearly in the video series). Of course, it is also used as a RAW processor, so we will be exporting our Photoshop editable files from it.
Lightroom can be used for these same functions, of course!
The main difference is that Lightroom has different "knobs and levers", and it would be quite difficult for me to make a double set of videos using Lightroom, so I've chosen Capture One, which is my preferred software, mainly because I have been using it for many years, and I am very comfortable with it.
I do feel that Lightroom is a bit less intuitive in terms of navigation, but if you are used to LR, that should be no problem!
The recommended exposure evaluation method for Lightroom is a little different, and in our "Lightroom PDF", you will be given a great workaround!
This simply means that you will have to be a little more careful with your highlight clipping, and to make sure that you have not over-exposed to the point of detail loss in the highlights. And, of course, highlight recovery is a very important tool which can be used to good effect. This is covered in my Foundation Course video, "Exposure Evaluation”.
Additionally, I do give Lightroom numbers equivalents in, for instance, the video where I explain how to create our white balance preset files, and a few other places.
Aside from that, and one or two minor differences in the tools (for instance, Capture One allows us to use adjustment layers, but we only use it for one image in the shooting sequence, and you can do the same thing in Lightroom using a graduated mask), there is no reason in the world that you can't use Lightroom!
As a matter fact, when I first started teaching six people at a time in my in-person workshops, everyone brought their own laptop with their own software, and we very often used Lightroom!