what are the chances of getting a hard wood cut from
an old lagestromia to root into a healhty tree
In most cases, older wood does not root as well as juvenile cuttings; this is not a hard and fast rule, just a general guideline; if all you can get is a hardwood cutting, don’t turn it down. If you have a shaded spot under a shrub, simply stick the cutting deeply into the ground; you should aim for at least half of the cutting into the soil.
The best time of year to do these kinds of cuttings is early in the spring because of the surge of life in the wood. Later on, there will be less vigor so they may not root. I would use a rooting hormone, or failing that, soak it in some willow tea; pour boiling water over some small willow twigs and let it cool, then soak the bottom of the cuttings in this.
I would probably do this for overnight, depending on the size of the cuttings. Then stick them into the soil. You could also cover the cuttings with a glass jar upside down over them to keep moisture in – only do this if there is no chance of the sun hitting it because that will just cook them.
Have fun with your experiment!