After being damaged, do eyelashes grow back?

Depends. If the lash root has been damaged it will not grow back.
Sometimes. Depends on the cause of the damage, but often the lashes will recover.

Related Questions

After being damaged, do eyelashes grow back? At which rate?

Yes. Eye lashes grow back unless the hair follicles have been damaged. Lashes grow at variable rates. Read more...
They grow back. If you just pull out an eyelash, it will grow back in about 3 to 4 weeks. If you break an eyelash while trying to pull it out, the broken eyelash will continue to grow. The only time an eyelash will not grow back is when the hair bulb is damaged, either by disease or injury. Read more...