There is a special Form I-765 that should be used in case you need to replace your work permit document. While filing the form you need to check the replacement box on the first page of the form, right under the Start here phrase.
EAD is the document that states that you have a legal right to work in America. What is more, some people do not even possess any other governmental identification documents so it is essential that you apply for its replacement straight away.
You can get a new EAD within three months. While you are waiting for it, you can use a copy of the lost one to proceed with your work. If you do not have the copy of an old document you can use I-797 Notice of Action or a confirmation receipt letter instead.
March 14, 2019