In a 4-qt saucepan, combine sugar, thyme, & 2 cups of water. Bring to a boil over medium heat & cook just until sugar dissolves.
Remove from heat. Add tea bags & let steep until room temperature. When cooled, strain syrup through a fine-mesh sieve into a large bowl. Add lemon juice & 1/2 cup water.
Process in an ice-cream maker according to directions, adding lemon zest in the last few seconds of churning. Scrape into airtight container & freeze for at least 2 hours. Makes about a quart.