Lightning network: how was malleability actually fixed?
As far as I know, the malleability issue was fixed with the Segwit soft fork in August 2017.


Yes.


  Was the malleability issue fixed with SIGHASH_NOINPUTor with some other method?


No, using SegWit.

SegWit stands for segregated witness. It's a generic and backward compatible change that results in signatures no longer contributing to txids. As the txids of previous transaction outputs being spent are included in what transactions sign, this indirectly results in malleation no longer resulting in the invalidation on descendant transactions.