Based on the community answers, Lightroom doesn’t offer a way to expand the canvas to preserve everything after this kind of transform. If the perspective correction pushes parts of the image outside the frame, Lightroom will effectively leave you with cropping.

The suggested workaround is to use Photoshop instead. In Photoshop, you can first make the canvas larger, then perform the transform/lens correction so the corrected image has room to fit without losing as much of the subject.

So the short answer is:

• In Lightroom: not really.
• In Photoshop: yes, by enlarging the canvas before transforming.

If possible, leaving more space around the quilt when shooting will still help, but with limited room the practical fix is to do the correction in Photoshop rather than Lightroom.