Examine the old lacing of the catcher's mitt. Notice the thickness of it. You can replace the lacing with the same size leather laces, or you can use a slightly smaller size to make lacing it easier. Though the thicker lace is stronger, if you do a thorough job of replacing the lace, your smaller-diameter lace will work just fine and be easier to string through the holes.
Order a spool of lace from a leather supply company. You can find these online. Your leather lace will come as a continuous length of leather wrapped around a spool for easy use.
Recondition the glove with saddle soap while you are waiting for your spool of lace to arrive. Saddle soap comes in a tin, much like shoe polish. It is clear or cream colored. Use a rag to dip some of the saddle soap out and rub it into the glove. A glove with lacing that has worn out probably has leather that needs reconditioning due to age.
Find the place on the glove where the lace has been knotted. Untie this knot. If it is tight and difficult to loosen, use a screwdriver and work it in between the layers of the knot to loosen it. When you get the knot loose, do not pull the old lacing out. It will be your guide for the new lacing.
Move about an inch ahead of the untied knot and pull the old lacing through the first hole. Insert your new lace material in the hole left by the old lace. As you pull the old lace out, keep following it with the new lace. In this way you will not get confused about the lacing pattern. Continue this procedure for the whole glove, not just the pocket. If the webbing gave way around the pocket, chances are it will give way in other parts of the glove, so replace all the laces at the same time.