Defining in Lightroom the drive space to be used by the computer.

What hard drives, internal and external do you have?

Is this a desktop or a laptop, or a All In One?

It depends on what is causing the low storage memory on the C: volume, and several things happen on import that could impact that.

Original files. If the imported original files are being directed to the C: drive by your Import dialog box settings, then consider changing your Import settings so that originals are stored on a different internal or external volume.

Previews. If you store the importing Lightroom Classic catalog on the C: drive, then all previews for images in that catalog are also stored on the C: drive, in the same folder containing the catalog. How fast the previews grow depends on several factors including your preview generation settings (in Catalog Settings, File Handling tab), and how many images you’ve browsed. Over time, the previews cache can grow to many tens of GB. It’s OK to throw out the …previews.lrdata file to regain all that space, because Lightroom Classic will automatically regenerate previews as you import and browse images. But some people don’t want to wait for preview regeneration, so they don’t like to throw out previews. For those people, it’s best to ensure plenty of free space on their catalog volume for the normal expansion of the …previews.lrdata file.

Catalog database file. If you store the importing catalog on the C: drive, then the catalog database itself can grow to several GB as you import more images and as image metadata accumulates.

Camera Raw cache. This is the most direct analog to the Photoshop scratch disk option, if that’s what you were thinking of. It’s the cache for images edited in the Develop module. But it’s the least likely to be causing your space problems, because the Camera Raw cache has a limit that I think is set by default to 5GB. The reason this is the least likely is that other components, such as the original files and their previews, are more likely to consume a lot more than 5GB of storage.

Taken together, what you can see is that the consumption of storage space on import can be because of some combination of the reasons above. There isn’t one catch-all answer because exactly which one is causing the biggest problem depends on how you set up Lightroom Classic, and which components you chose to store on your C: drive vs on another volume. 

All my imports go to an external SSD to limit how much storage space is lost on the boot volume as I catalog more images with Lightroom Classic.

Another possibility is that RAM is running low, causing Windows to expand its VM page file on the boot volume, and if free space is already low enough, an expanding temporary file that comes close to filling the volume could trigger the warning. But this is probably only likely if the computer has less than 16GB of RAM.

You have mentioned two different things. 1. Drive C: space and 2. Ram. The PS memory space settings apply to ram. Your issue is drive C: running out of space. Lightroom Classic uses more and more drive space as photos are added, in the form of growing catalog size and also the space taken up by the previews that Lightroom Classic creates when you import photos.

Please provide information on the type of Win 11 machine you are using so the group can recommend solutions.  I sounds for sure like you need additional drive space, but there are several ways to do that depending on your actual hardware.