Those sound like the tape I use.

After you apply the tape, you have to really press the tape down onto the lace to get it to attach. Try using a straight edge of some sort to rub over the tape so that it sticks even better. A ruler or the edge of a scissors or something that you can slide over the strip will made it grip when you apply the pressure.

Then try to peal off a small edge, and then pull towards the side, not upwards. Pulling up will rip it from the lace. Try pullling the paper off the lace with a sideways direction.

See how that works!

P.S. Make sure the lace is dry and does not have any alcohol or lace release on it. This can hinder the adhesive.