Nope. I don't even know why there's so much arguing about LSS and all.
The first mention of legendary super saiyan is just a form. The form itself is legendary, not a person. Then we hear Vegeta call the person who got said form the Saiyan of Legends. So it's fucking BOTH of them, the saiyan of legend is just the guy who unlocked the SSJ form, which is a legendary form, 1000 years ago. It's not hard at all. The only thing that super did/is going to do is give the saiyan of legend a name, aka Yamoshi, and also add to the fact that he also became SSG along with SSJ.
Broly is TOEI non-canon so whats the fucking point of even bringing him into anything?