How can you even claim that a champion who can't pull off a duo lane can actually pull off a solo lane?
Do you realize why Lulu is even picked as a mid or top champion and not as a support? Almost all other supports are not mid laners because of their base stats or poor scalings and Lulu ignores this + her utility makes it impossible for her to get ganked and she can trade just as a mage can.
She is good as a solo laner because then she gets to access a solo laner's gold income, which in turn gets her the items needed to boost her damage up and utility, effectively turning into a second support with just one of her skills, not to mention that she doesn't switch between these 2 roles but she does them at the same time.
Riot is trying to reinforce her as a support mage - which means that if you want to take her mid, you don't take her as a mage but as a second support that has more gold than the real support. Which is the exact reason why Lulu is getting so much popular.