Wrappable textile sleeve having supplemental lace closure and method of construction thereof

A wrappable textile elongate wire harness sleeve for protecting the elongate wire harness, comprising:

• a wall of interlaced yarn having opposite edges extending in a lengthwise direction along a longitudinal axis of the sleeve between opposite ends, said interlaced yarn being woven with warp yarns extending in said lengthwise direction and weft yarn extending generally transversely to said lengthwise direction, said opposite edges being wrappable into overlapping one another to form an inner tubular cavity, said wall having a plurality of closed loops extending along the length of said wall, said plurality of closed loops providing a first set of closed loops positioned adjacent one of said opposite edges and a second set of closed loops positioned adjacent the other of said opposite edges;
• at least one flexible lace extending through said first and second sets of closed loops in zig-zag relation from said first set of closed loops to said second set of closed loops, wherein said at least one flexible lace facilitates drawing the opposite edges into overlapping relation with one another and to maintain the wall in a closed state;
• and
• wherein said first and second sets of closed loops are formed from at least some of said warp yarns.