if there is any transportation that go directly from lugu lake to chengdu?

I'm afraid there is no direct transportation. You are advised to first take the bus from Luguhu to Xichang. The ride may take about 6.5 - 7.5 hours. The bus schedule are 07:40, 08:00, 08:30. 09:00 and the price is CNY95 per person. The timetable and ticket price is just for reference.

Then take the direct bus in Xichang tourist distribution service center to Chengdu. The buses depart from 07:00 to 17:00 and the ticket price is CNY192/ person. The ride may take about 8 hours.