The confusing part is choosing the best account. Below is a screenshot of the registration page.
If you'll be using it quite a bit with students, you (the professor) can request an educational upgrade for the class on this page. Make sure you are using your edu email account though. The educational account is the equivalent of a Team account (see screenshot below). The professor first has to sign up for LucidChart and login. The request is sent and you will get an email from firstname.lastname@example.org that contains a URL to give the students to sign up. You could just forward the email or post the URL in D2L.
There is free account to use without having to request anything, but the functionality is limited. If LucidChart will be used for just one or two basic assignments, the free account is probably ok but when I made one complex chart I filled up my account.
Be careful to avoid accidentally signing up for the free trial of one of the other accounts.
It is possible to sign in with Google or Yahoo to avoid creating an additional account just for LucidChart.
We tried to get an account for the whole university so anyone with a uwec.edu account would automatically get the upgrade but, unfortunately, it doesn't work like that. If the university has Google Apps for Education, integrating is possible so students don't need additional accounts. From what I understand, simultaneous/collaborative editing is only available if Google Apps is integrated (meaning, multiple people cannot work on the same LucidChart from different computers at the same time). We do not have Google Apps for Education at UWEC, but some UWs do.