Nope! You do not need to have Google Classroom or any other LMS to use Classwork.com. 

When you create an assignment in Classwork.com, you'll receive a link to share with your students. That's all they need to access the activity. You can share the link however you like -- by email, posting it online, or even displaying it on the whiteboard.

Students simply click the link to open and complete the assignment. On the assignment screen you can choose settings to collect names, IDs, or emails, so you can keep track of your classes without an LMS.

Classwork.com does integrate smoothly with Google Classroom, so if you use it, you'll have the best of both worlds!