Yes and no! If you are accessing Duolingo via the web or the Android and iOS apps, you will need to be connected to the internet.
If you are a Duolingo Plus subscriber, you can access a handful of lessons for offline use, all within your iOS and Android app. Just a heads up, you'll need an internet connection to start the downloading process. Once you've downloaded your lessons, you can set your device to offline mode.
For a step-by-step process on how to download offline lessons, click here. Wanna be a Duolingo Plus subscriber? Learn more here.