I then washed them a couple of times to check for colour fastness. I am very happy with the colour of the lace. The lining is pale, not as pale as the photo but pale just the same. I'm going to have another go as I didn't check that the thickened dye had penetrated the fibres before heat setting.
Could be that the dye just isn't suitable for the fabric. But now I know that I can dye nylon lace quite successfully with thickened dye.