JSXGrpah is distributed under a choice of licenses. The use of an "LGPL AND MIT" on their home page is a bit misleading as I could be led to think that both licenses apply:
JSXGraph is released under the LGPL – Lesser GNU General Public License – and the MIT license.
However the actual COPYRIGHT file included in the repository is more explicit:
JSXGraph is free software dual licensed under the GNU LGPL or MIT License.
You can redistribute it and/or modify it under the terms of the
- GNU Lesser General Public License [...]
What this means is that I can select one license or the other.
yet, in all cases some portion of the code are always under the MIT license as I can see here. The code "UTF-8 Decoder by Bjoern Hoehrmann" was itself originally under a choice of BSD or MIT license. Since only an MIT license has been reproduced in the JSXGraph COPYRIGHT file, I assume that the JSXGraph authors elected to use the MIT alternative.
As a summary I can select either the LGPL3.0 or later or the MIT license, plus the MIT license for third-party inclusions.
Both licenses allow unrestricted usage. The LGPL has extra requirements including source code redistribution and change tracking when modified. Using one over the other is a matter of taste and legal policy. For a proprietary application, the permissive MIT license has fewer constraints.
Suppose I build a subscription-based website that allows users to buy monthly access to the site. Users would be served proprietary content and be able to interact with dynamic widgets built on JSXGraph. What responsibilities do I have to customers or the license holders themselves?
I would also signify my choice of license by stating that I elected to use the MIT choice: This would be an extra statement that I would add to the notice I reproduce or it could be part of some additional documentation.
Does the answer change if instead of a website, I build a mobile app that serves the content and dynamic widgets?
If I pick the permissive MIT license, then the requirements are essentially limited to attribution and the same as they would be for a web application frontend as described above.