This is most commonly caused if you are using a version of Blender bellow 4.1.0. Make sure to update your Blender version and try again. If you can't update, try to use some of the older versions of Stylized Hair PRO add-on.

This is caused by parenting the base mesh for the hair strands to your character via the 'Armature Deform' method (ex.: Ctrl P > Armature Deform > With Automatic Weights). Instead, parent to a deforming bone directly: 1. Remove any existing armature deforming modifiers. 2. In Object Mode, select the hair base mesh, then the armature. 3. Go to Pose Mode, select the deforming bone (ex. the Head or Spine bone) 4. Then parent with Ctrl P > Bone.

The most common issue for a laggy scene when working with the add-on is a dense base mesh for the hairs. Try to use as low-poly base mesh as you can. Also, make sure you have a clean UV map on the base mesh, without any overlapping UV islands. Don't add your hair strands directly to your character mesh, make a separate base mesh. Also, try lowering the resolution of the generated mesh, by going to the SETTINGS panel and reduce the hair or profile resolutions.