The Eng. word 'lace' comes from Lat. laqueus, a 'snare,' and is used in that sense in Old Eng. It is then employed for any cord or hand, and that is its meaning in Ex 28:28,37; 39:2 f., Ex 39:31, Sir 6:30.
And they shall bind the breastplate with its rings to the rings of the ephod with a lace of blue, that it may be above the girdle of the ephod, and that the breastplate be not loosed from the ephod.
And thou shalt put it on a lace of blue, and it shall be upon the turban upon the front of the turban shall it be.
And he made the ephod of gold, blue, and purple, and scarlet, and twined byssus.