In a solo lane just W yourself and slow things, congrats you have escaped a gank. Oops, can't escape? Who cares, just be a support afterwards, and blindly build AP. The enemy laner/jungler only gets one kill at a time, so screwing up isn't the end of the world. Very little risk involved overall.
In bot lane, you can't do that, therefore already adding to the already risky gameplay in lane. Oops, can't escape? Both parties usually die, so usually 2 kills at a time. Enemy x, then, starts to snowball quickly because you thought you can just play her like you're Lulu top, and is usually hard to shut down unless one of your teammates is really fed. Because you are underleveled (that's just a support thing due to no farming), it is a little harder to catch up, therefore you have to play even safer. Same reason why people perceived Sona as "bad".
Escaping ganks alone is easy, but escaping ganks with very limited tools AND getting another person out alive at once is not. The latter is the risk that Lulu supports get, while she does not have to do any of that as a solo laner. Because of no "having to save that shitty teammate while having enough just for yourself" in a solo lane, Lulu solo is very safe compared to her support counterpart.