If you want to use it in this context, feel free, but It sounds stupid. A path is something you lay down, not set up.
But they didn’t lay down the path. The physical structure of the path was already there. They changed the status of the path from parking to bike lane. Hence, they erected the bike lane.
Hyper-pedantically (which is to resist the evolving meaning of words), one erects a monument but builds a building. When you build a cathedral, or capital or headquarters, you simultaneously erect a cathedral building, capital or headquarters, so the words often overlap. But one builds a church when they erect a parish.
Remaining hyper-pedantic, there’s a common misuse of a word that people think is a medical term, but it’s not. The correct word is priapism.