I have just made my first batch of cake lace which worked perfectly.  I put it between two sheets of baking parchment as I didn't have any greaseproof paper, when I looked at it two hours later it had become floppy and when I picked it up it stuck to itself.   Where did I go wrong, should I not have used the baking parchment????

I have not had this issue...and I don't know which lace mix you used....I use Sugar Dress with no issues.  I usually just layer mine between paper towels on a sheet pan with a plastic lid....I have some in the storage room right now that was made in April and it's still perfectly usable.  I'd let it dry when you remove it from the mat a few minutes on both sides before storing.