I would say Lux wins this matchup just because of her range and poke. Lissandra's Glacial Path (E) is a pretty slow traveling spell and Lux would probably be able to walk out of it's range if positioned correctly.
Ulting Lux in a teamfight would be suicidal because Lux is always far behind her team.
Prismatic Barrier (W) Is also great for dealing with lissandra's poke.
That is just my opinion (I'm a platinum V Lux main).
Of course you can't call Lux a counter to Lissandra because she only has a minor advantage over Lissandra and if played incorrectly Lux is always easy to kill.
I hope I could clear things out for you.
Tell me if you have any more questions for me.
(Also please forgive me for my rhetoric skills. English is not my native language)