Thanks for writing. It depends on what type of lawn weeds you have. If they're annual weeds, like crabgrass, then you can use a product containing corn gluten. You need to use it early in the season --- like around the time the forsythia blooms --- to stop those annual weed seeds from sprouting.
If they're perennial weeds though, there aren't any great pet-safe options. That said, if you maintain a healthy lawn (letting it grow at least 2 inches tall, watering it in drought, feeding it regularly, and aerating yearly), it will do a pretty good job of controlling perennial weeds on its own.