Pat
I don't think I would mess with trying to strectch precut lace. Unless you plan on cutting it down more after stretching to get a uniform string.
When I cut strings I cut them wider to allow for the shrinkage due to stretching. I can then cut to my final width. On smaller items like bracelets, hatbands, key fobs , and such I may not stretch the string at all. Especially if its pretty firm.
Mike