"Везти" with the meaning of "bringing luck" comes from the noun "везение", and it probably isn't connected etymologically to its homonym "везти" = to carry. I think it's just a coincidence that they're identical.
There's a hypothesis that it came from French ("avoir de la veine" = to be lucky). Read here: https://vk.com/@algoritmy_vezeniya-otkuda-k-nam-prishlo-vezenie
Another speculation is that it's connected to the verb "вязать" (to weave), and in that case it might refer to the Slavic mythology and Mokosh goddess, who was a "weaver of fate". Full explanation here: https://rus.stackexchange.com/questions/19779
My personal hypothesis is that it comes from the stem "ведать" (to know), and more specifically its derivative "ведьма" (witch). The reason I think this, is that "luck" implies good things that happen to you by chance (not because you deserve them), and it wouldn't surprise me that it could be seen as a contract with the devil or black magic.
And another version, which sounds a bit crazy even to me, deals with the fact that "везение" sounds a lot like "Вельзевул" (Beelzebub). Again, it's all about the devil's schemes, haha.