Am I understanding it correctly that LN only works with segwit?
Why would it work only with segwit? I see no technical reason, but segwit adoption would certainly help LN to make opening/closing LN channels cheaper.
LN as it is now depends on transaction malleability being fixed. That's why it was designed with segwit as a prerequisite. So yes, Ibian, you are correct as far as the real current Lightning Network goes.