Afaik transaction malleability breaks LN. So Segwit is necessary for LN as it fixes transaction malleability. Also BIP 114 for MAST requires Segwit.
I think that the malleability bug is separate from the segwit. I think segwit required the fix in order to work. So segwit in on itself is not required for LN.Segwit is ABSOLUTELY needed for LN to work.
In current implementation, sure. But conceptually, no. Don't take my word for it - gmax said so XD. 'Something like LN' is simplified by a malleability fix. But not utterly dependent upon. And segwit is but one of many possible malleability fixes.