Leggy mountain laurel
Mountain laurels regenerate very slowly after heavy pruning, so a better way to go about it would be to prune back portions of the plant gradually over 2 to 3 years. Dead branches can be pruned out at any time year. Pruning cuts to healthy branches must be made prior to bud break in the spring for best results, according to NC Cooperative Extension (https://polk.ces.ncsu.edu/pruningcalendar/). This will result in loss of some of the spring season flowers, but results are better if the pruning is done before bud break. Pruning helps to stimulate new shoots and may help renew the plant to begin flowering again.
You might also want to test the soil in this area. Mountain laurels like it on the acidic side (pH 4.5 - 5.5). Here is information about how to do a soil test. https://extension.umd.edu/hgic/topics/soil-testing
In addition, remove the invasive English ivy from around the base of the plant. This will reduce competition for nutrients and water.
Thank you very much, Christa. This is very helpful.