Lay the curtain flat on your table or work surface, with the lining side facing up. Locate the seams where the lining is sewn into the curtain.
Rip out the seams along the bottom and sides of the curtain, using a seam-ripper tool. Insert the point of the tool behind a stitch, taking care not to pierce the fabric. Slide the ripper forward to sever the thread. Repeat until the seams are ripped out. Pull out any hanging threads.
Inspect the seam at the top of the curtain. This seam varies depending on how the curtain is hung, such as tab-top or rod-pocket curtains. Rip out the seam if it's located below the curtain hangers. Cut the liner off in a straight line, just below the hanging section, if the liner is sewn in above the hangers.
Cut out a new liner from heavy-weight fabric, using the old liner as a template. Make the new liner 1 inch longer than the old, if you cut it off below the hangers. Make the new liner the same size if you removed the old liner at the top seam.
Fold down 1 inch of fabric along the top of the new liner, folding it toward the wrong side of the fabric, if you cut off the old liner. Press the fold with a hot iron.
Pin the new liner in place on the back of the curtain. Fold the edges of the curtain over the liner, as they were on the old liner. Line up the folded top, if applicable, below the curtain hangers, and pin it in place.
Sew the liner in place using thread that matches the front of the curtains. If your liner top is folded, make a straight stitch within 1/4 inch of the fold. If you keep the stitching straight and use matching thread, this new line of stitching on the front of the curtain won't look out of place.