But what if the source code is modified? Will the users still get the usage right of the patents? And what if the source code is modified so much that the original code is barely recognizable? It seems to me that using this license means you're giving away your patents for free.
What you describe would be a 'derivative work', as mentioned in the second paragraph.
It might be clearer if it was capitalized like in the MIT license, but I think it's pretty clear as it is.
Will the original authors still have copyright over it?
If yes: Then clearly in the mind of the law the original work is still present.
If no: Then the license choice of the original authors is not longer relevant.
Other licenses, like Apache, include patent grant withdrawal clauses, where you can lose the right to use the patent if you initiate a lawsuit.
The notorious Facebook BSD+PATENTS license includes a similar withdrawal of patent grant, but for any Facebook patent, not just something related to the software in question, and also only if you sue Facebook or a subsidiary — the Apache withdrawal applies to "any entity".
Here, there are no withdrawal provisions, hopefully giving you that full confidence as a user. As an author, if you have a patent on something, and then you release an open source project under LIL that uses that patent, you give up the right to sue anyone for infringing on your patent by using your open source project, period.
I think that's more in the spirit of open source.
This is not true. The Facebook PATENTS grant terminates if a patent assertion relating to the software is made against against "any party".