Wait for her to use her black shield before you start wasting cc. If you manage to hook even when she black shields and if you can make a play, fly in and wait for the shield to pop/disappear, then flay.
When playing Lulu, just pray she doesn't dark bind you and if she black shields herself the turn the enemy adc into a squirrel. If she black shields the adc, then turn her into a squirrel. I like to rush Talisman on Lulu support after Sightstone, so if you can do that vs morg, it's better than Frost Queen. Reason for this is that as soon as Morg uses her ult, you can use Talisman to disengage and to gain enough distance to break the chains so she doesn't stun.
Ultimately, try to avoid her darkbinding, as it allows her ADC to auto you. You can still cast spells if you do get binded, so if there's anyway you can keep the ADC from dealing damage to you/your ADC during this time period, take advantage of that (i.e. counter their trade).
I haven't played the matchup much, but I think if you're playing Thresh support, you technically have a better advantage. Lulu support, not so much. Also don't ult as Lulu if the person closest to yourself/teammates is blackshielded (if you wanna peel).