Can lissandra go support?

Its doable, but not the most effective role for her.

She has the CC to be a decent engage support, But due to the lower gold income from the role, you will typically be forced into a tanky front liner instead of burst mage. Her only problem bottom lane is lack of range on her harass, and if you aim it through the waves for better range, you'll end up pushing the waves harder and attract a wild jungler.

So in short, yes she can support. But its not really her best role.