As I know, there is no direct public transportation available from Emeishan City to Lugu Lake. Usually, you have to transfer at Xichang. Here is the way:
Firstly, please take a train from Emeishan to Xichang City. It is suggested that you take a night train which will arrive in Xichang around 5am the next morning. The train schedule could be searched here: https://www.travelchinaguide.com/china-trains/

Secondly, at Xichang Railway Station, please take a cab or city-bus to Xichang Tourism Bus Station (西昌旅游客运站). This bus station supplies one coaches to Lugu Lake at 07:30 everyday. The rough journey is about 7 hours, costing CNY75. The bus terminal is at Luguhu Town, a little far from the lake. So, you could hire a local van to stay one night at Lige.