Do you need a license to sell laser-engraved goods?

Generally you can sell handmade goods with the same basic requirements as any small side business in your jurisdiction — commonly a local business registration and collecting/remitting sales tax where required. Many makers start as sole proprietors on Etsy with exactly that.

The sharper legal edge is intellectual property, not licensing: engraving trademarked logos, characters, or team marks you do not have rights to is infringement even "just on Etsy." Sell your own designs. (Not legal advice — rules vary by location; check your local requirements.)